Orphism was one of the mystery cults of ancient Greece which developed in about the 6th century B.C.E. The cult takes its name from Orpheus, a figure from mythology who was known for his poetry and musical talents. Orphism can best be characterized as a counter-culture movement, with central tenets such as alternative myths, a life of strict purity, including ascetic practices such as vegetarianism, and the belief in reincarnation. It is precisely their version of reincarnation that so easily answers the question put forth as the topic of the season: Why, if we have free will, do we keep coming back to Planet Earth?
To the ancient Greeks, reincarnation was usually called the transmigration of the soul. This belief was not the sole property of the Orphics, as we find others believed in it also. We read about it in relation to famous figures such as Pythagoras and his followers, Pindar, and Plato. It is interesting to note, however, that the belief remained largely identical, no matter in which circle it was discussed. However, the only context in which it can be fully explained is in Orphism.
In order to understand this Orphic belief, we must first turn to one of their central myths, that of the dismemberment of the infant-god Dionysos Zagreus:
Persephone was impregnated by her father Zeus who had transformed himself into a serpent. The result of that union was the baby Dionysos Zagreus. It was foretold that Zeus would pass his position as King of the Gods onto this son. The Titans, already angry with Zeus for dethroning his father Kronos, took their revenge out on Dionysos Zagreus: they caught hold of the child and violently dismembered him. Afterwards they first boiled and then roasted the pieces, and feasted. One piece, however, was not eaten, namely his heart. Athena found this remaining piece, and hid it in a covered basket, which she then brought to Zeus. Zeus, furious at what had been done to his youngest child, struck the Titans with his thunderbolts, and set them ablaze. Their bodies were reduced to ashes. The race of humans was then created out of these ashes.
From this, we learn that our constitution is part Titanic (due to the bodies of the Titans) and part Dionysian or divine (due to the dismembered god being in their stomachs). The Titans, being the children of Ge, the Earth goddess, create our physical bodies, while Dionysos gives us our divine element: our souls. About this myth, M.L. West writes, The fact that the Titans had eaten Dionysos was merely evidence of their wickedness It is to the living Dionysos that we must turn for salvation. 
For one who is familiar with Greek literature, you may recall that one recurrent theme is inheriting the guilt of our ancestors, especially blood-guilt. Take for instance the case of Orestes, which is brilliantly retold in Aeschylus Oresteia, written in the 5th century B.C.E. Agamemnon, the father of Orestes, returns home from the Trojan War. His wife Clytemnestra, who had been unfaithful to him, devises a plot with her lover that they will kill Agamemnon. She carries out her plan. Orestes, according to tradition, must avenge his father's death. The only way to do so is to kill his own mother, which he does. However, it is also a great crime to kill one's mother, and this act must be avenged. Since there is no one to further inherit this duty, such as a child of Orestes, the duty now falls to the Erinyes (also known as the Furies). They are goddesses who punish those guilty of killing blood relatives, among other things. Their only desire is to exact justice on the guilty party. They tormented Orestes in an effort to drive him mad. The story ends when Athena intervenes, deciding that Orestes was justified in avenging his father's death. Thus, there is no further blood guilt.
This myth is fascinating, not only because it provides the archetype for our modern-day penal system, but also because it highlights a belief that parallels reincarnation. The fact that blood guilt can be inherited from one of our ancestors lies at the root of the cause of reincarnation in the Orphic tradition. Because our ancestors, the Titans, killed the god Dionysos, we inherit that guilt.  Thus, we are responsible for atoning.
There is a passage in one of Pindar's poems that hints at this: But those at whose hands Persephone accepts atonement for (her) ancient grief, their souls in the ninth year she sends up again to the sun of this world.  The ancient grief is the killing of Dionysos by the Titans. To send our souls up again to the sun means to reincarnate. In Greek literature, phrases such as in the darkness or where there is no sun are often used to mean the Underworld. To be in the sun means to be on earth, alive. Thus, the only way one's soul can be sent up to earth again from the Underworld is for it to reincarnate.
We also have a quote from Plutarch which echoes our explanation. He says,
It would perhaps not be wrong to begin and quote lines of Empedocles as a preface For here he says allegorically that souls, paying the penalty for murders and the eating of flesh and cannibalism, are imprisoned in mortal bodies. However, it seems that this account is even older, for the legendary suffering of dismemberment told about Dionysos and the outrages of the Titans on him, and their punishment and their being blasted with lightning after having tasted of the blood, this is all a myth, in its hidden inner meaning, about reincarnation. For that in us which is irrational and disorderly and violent and not divine but demonic, the ancients used the name, Titans, and the myth is about being punished and paying the penalty. 
Plato also uses a curious phrase that can only be explained in this light. He said that humans who have contempt for oaths and religion had in them a Titanic nature of which our old legends speak. 
At this point, we have clearly established that humans have a dual nature. We have inherited the blood guilt from our ancestors. This guilt, however, can also affect us physically. Plato explains that we can fall terribly ill due to some ancient sin.  This sounds pretty fatalistic. Is there anything we can do?
One thing that will allow us to atone is purity. This includes undergoing ritual purifications, as well as living a life of asceticism. In the Republic Plato says that Orphic priests can expiate and cure with pleasurable festivals any misdeed of a man or his ancestors.  Making offerings to the gods, especially to Persephone, is also important, as shown by the Homeric Hymn to Demeter. Here, Haides says to Persephone, Those who defraud you and do not appease your power with offerings, reverently performing rites and paying fit gifts, shall be punished evermore.  Plato also agrees with this sentiment, saying, Terrible things await those who have neglected to sacrifice.  A surviving Orphic document says, This is why the magi perform the sacrifice, as if they were paying a penalty. Unfortunately, we don't know much about the actual rituals. So far, archaeologists have only unearthed one fragmentary script of a ritual, believed to be Orphic. Two lines read: Accept ye my offering as the payment for my lawless fathers. Save me, great Brimo.  Some scholars have imagined what the rituals might be like:
Imagine, for instance, a nocturnal ceremony, torchlit. A boy is to be initiated. He sits bravely on the throne. The Kouretes or Korybantes dance round him, round and round, noisily clashing their swords on their shields. A priestess plays endlessly on the raw-toned pipes. After a time the circle is penetrated by the ghastly white-faced figures of the Titans, man's ancestors. They prowl about the boy, flashing a mirror before his face. He follows it as if hypnotized. The music goes on, becomes wilder, with drumming, and the uncanny braying of bull-roarers. Knives glint over there in the gloom, there are inhuman screams, hacking and wrenching of limbs. The holy casket is carried round, and everyone sees the hot, bloody heart it contains. There are smells of roasting flesh. Presently there will be meat to eat; meanwhile we all bewail the savage murder of that innocent child. By way of consolation an effigy is produced, made of or coated with gypsum. The heart is inserted into its chest. Stark, white and lifeless the thing stands there in the flickering light. Then the miracle. In a moment of blackout or dazzling light the place of the effigy is taken by the new initiate, himself now covered with gypsum like his former murders, and he springs up alive and well, ready to enter on his new life. 
Once we receive these purifications and have made our offerings, we must keep ourselves in this state of purity. For this, ascetic practices were recommended. The Orphics were known to reject materialism, and to especially have a disdain for the physical body. Again, we use a quote from Plato to illustrate the point:
And does not purification consist in this, which was mentioned in the ancient word, to use all our means to keep apart the soul from the body, and teaching the soul the habit of collecting and holding on itself, away from all bodily elements, and remain, as far as it can, both in the present as well as in the future life, alone in itself, intent to its freeing from the body as from fetters? 
The Orphics had a saying, soma-sema, by which they meant to convey that the body is a tomb or a prison for the soul. This belief is attested by many ancient authors. Plato has explained it best, as in this passage:
Some say, in fact, that the body is the tomb (sema) of the soul, as if at present it were buried there. On the other hand because through it the soul expresses all it expresses, it may thus rightly be called a sign (sema). It seems to me, however, that primarily the followers of Orpheus have given it this name; almost as if the soul is undergoing atonement for sins it must expiate and has around itself this enclosure, semblance of a prison, in order to be guarded. Such a prison therefore, as its name suggests, is a case (soma) for the soul until its debts are paid, and nothing needs to be changed, not even a single letter. 
Thus, we must reject this material world, as it only represents for us the imprisonment of our soul in a material body, which is our punishment for the inherited blood guilt of our Titan ancestors. Empedokles says that the soul is clothed in an unfamiliar garment of flesh. 
So far, we have heard very little mention of free will in the discussion. We inherit the guilt of an action that we ourselves didn't commit. We are punished because of it, forced to reincarnate on the Earth. All of this is quite against our will. At what point do we make a choice? We shall now turn our attention to the choices we can make.
Orphic teachings explain that upon one's death the soul is taken to the Underworld. After walking along the path for a little while, we will come to a fountain next to a brilliant cypress. Although we will be very thirsty, we are not to drink from this fountain, because it is the water of Lethe, Forgetfulness.  Instead we must pass by this one, and only drink from the second fountain, called Mnemosyne, or Memory.  This is a very important decision, because if we drink the waters of Lethe, we will forget; if we drink from Mnemosyne, we will remember. Remember what? Our last life on Earth. We will remember whatever lessons we have learned, and we will remember how hard we worked to keep ourselves pure. However, there are guardians at the fountain. They will only allow us to drink if we know the correct thing to say, which is, I am a child of Earth and Starry Heaven. I am dying of thirst. Now let me drink from the cold waters of Mnemosyne. After this, they will allow us to drink, and we will retain our memories. 
The above instructions were engraved on a small gold tablet that was buried in the tomb of an Orphic. Several similar tablets have been found with similar ideas on them, although none of the tablets have identical wording. It is not clear exactly how one acquired a tablet, but the most reasonable explanation is that it was given to the person by an Orphic priest, possibly after initiation.  Nevertheless, it served as a powerful tool for the soul in the Underworld, for without it, we would not know which fountain to drink from, nor would we know what to say to the guardians.
Although it is not explicitly stated in the above mentioned tablet that Persephone is one of the guardians, we may assume that she is. In another Orphic tablet we have a description of the deceased person meeting Persephone. The deceased person is supposed to say the following:
Pure I come from the pure, Queen of those below the earth;
and Eukles and Eubouleus and the other gods and daimons;
For I boast that I am of your blessed race.
I have paid the penalty on account of deeds not just;
Either Fate mastered me or the Thunderer, striking with his lightening.
Now I come, a supplicant, to holy Phersephoneia,
that she, gracious, may send me to the seats of the blessed. 
Another gold tablet from the same area says, For I too claim to be of your blessed race.  By declaring that we are of your blessed race we are referring to that part of us which is divine, our soul. Instead of explaining who we are in terms of our job or our family, we define ourselves in terms of a lineage of the ritually purified and in terms of a link with the gods.  We declare that we have paid the penalty by undergoing purifications and living a life of asceticism. If we truly have achieved such a state of purity and atonement, we can ask Persephone that she sends us to the seats of the blessed. Another recently-discovered text says, Enter the holy meadow. For the initiate has paid the price.  This is the part of the Underworld where only the most pure will go. [H]e who arrives there [i.e. in the Underworld] purified and initiated shall dwell with the gods.  Once we go there, we will not return to Earth. The only reason for us to return is to continue to pay the penalty. However, once this is achieved, we are released from the cycle of life, death, and rebirth: But I have flown out from the circle of heavy grief. 
When we were on Earth we were of two natures, material (Titanic) and divine (Dionysian). Once we have shed the material, only our souls remain, which are divine in nature. Thus we ourselves become as the gods. Empedokles is well known for bluntly saying, For already have I once been a boy and a girl, a fish and a bird and a dumb sea fish.  He also explained that he was a daimon or divine-spirit who was rejected from the realm of the gods due to his foolishness, and now continues to incarnate in different bodies on Earth until he makes the correct choices and finishes atoning. As Edmonds explains, the purified deceased need not think of penance, but rather she may, because of her preparations in her mortal life, expect to realize her own divinity. 
Thus, in this brief article we are able to see that the reason we keep returning to Earth is because we choose not to use our time here to atone for the inherited blood guilt. Furthermore, unless we receive purifications and instructions from an Orphic priest, we won't know which fountain to drink from, or what to say to the Queen of the Dead. Unless we follow the correct course of action, we set things in motion for us to return here again and again.
1 West, M.L., The Orphic Poems, Clarendon Press, Oxford, 1983, p. 166.
2 Perhaps one might here object, by saying, This is all quite interesting, but remember that Aeschylus wasn't an Orphic. You can't use his play to argue your point. He probably wasnt an Orphic, but he certainly was familiar with their beliefs and myths. I am quite confident of this for a number of reasons. Aeschylus was born in Eleusis, the home of the famous mystery cult of Demeter and Persephone, the Eleusinian Mysteries. He is called the Father of Greek tragedy. In general, dramas were performed for the god Dionysos, the god of theater, and also the god of the Orphics. The state began to sponsor such dramas in the gods honor in the 6th century, the same time that Orphism seems to emerge. Aeschylus also fought in the military, and visited Sicily at least twice, perhaps three times. It is said that Zeus gave Sicily to Persephone as a wedding present, and at least one version of the myth says that Haides abducted Persephone in Sicily. Persephones cult was quite strong in Sicily, and all of southern Italy is known to be very influenced by Pythagoreans and Orphics. Furthermore, at the end of the Oresteia, the Erinyes are calmed, and changed form. They are then known as the Eumenides. In the Orphic Hymn #70 the Eumenides are said to the daughters of Persephone. The Erinyes were said to wear black, have snakes for hair, and had blood dripping from their eyes. One of Demeters cult titles was Erinys, or raging. She was pursued by Poseidon, in the form of a horse, who eventually forced himself upon her. From that union she gave birth to the horse Arion. (This myth has parallels with another, in which Poseidon mates with Medusa, whose appearance is rather like that of the Erinyes. She gives birth to Pegasus, the flying horse.) And finally, bear in mind that the oldest telling of the Orestes myth is in Homer, where Orestes kills his mother, and he is believed to be justified in doing so. There is no further pursuit by the Erinyes as in Aeschylus version. All of these details demonstrate an interest in the goddess Persephone, and the mystery cult of Orphism.
3 Pindar Dirges Frag. 133
4 Plutarch, De Esu Carn. 1.996b-c
5 Plato, Laws, Bk. III 701b-c. Plato is not only thought to be highly influenced by Orphism, but he also is the most important preserver of Orphic practices and doctrines.
6 Plato, Phaedrus, 244 d-e.
7 Plato, Republic, Bk. II 364b
8 Homeric Hymn to Demeter, 364-369
9 Plato, Republic, Bk. II, 365a
10 Derveni Papyrus Column VI, as translated by Gαbor Betegh, The Derveni Papyrus: Cosmology, Theology and Interpretation, Cambridge University Press, Cambridge, 2004.
11 From the Gurτb papurus, 3rd. century B.C.E. (Reconstruction as per West, p. 171) Brimo is another name for Persephone.
12 West, p. 163
13 Plato, Phaedo, 67d
14 Plato, Cratylus, 400c
15 Empedokles, frag. 126
16 It was a common belief, among many cultures, that the dead are very thirsty.
17 This is from the Gold tablet from Hipponium.
18 I wanted to include this interesting quote on the subject of memory: [T]he central place given to memory in eschatological myths indicates an attitude of refusal with regard to temporal existence. Memory is exalted because it is the power that makes it possible for men to escape time and return to the divine state. Vernant, Jean-Pierre, Myth and Thought Among the Greeks, Routledge and Kegan Paul, London, 1983, p.88
19 Initiation and purification are often used interchangeably in an Orphic context. (Nilsson, Martin, Early Orphism and Kindred Movements, Harvard Theological Review 28, 1935, p. 208.)
20 From Thurii, 4th C. BC (usually labeled A2) .
21 This tablet is also from Thurii (usually labeled A1) .
22 Edmonds, Radcliffe, Myths of the Underworld Journey: Plato, Aristophanes, and the Orphic Gold Tablets, Cambridge University Press, Cambridge, 2004, p. 109.
23 Gold Leaf found in Thessalian Pherai from 4th C BC.
24 Plato, Phaedo, 69c
25 Gold tablet from Thurii (A1)
26 Empedokles, frag. 117
27 Edmonds, p. 99.