The Pythagorean idea of reincarnation is the result of the influence of Orphism. The Orphics thought that life on earth was an expiation for crimes or impurities of previous lives. They were dedicated to the idea of katharsis, ‘purification’ of their souls.
Edinger identifies Orphism as the generative religious source for Pythagorean metempsychosis and ascetic purification, reading its doctrines as depth-psychological archetypes of the soul’s expiation and liberation.
, The Psyche in Antiquity, Book One: Early Greek Philosophy From Thales to Plotinus, 1999thesis