Because the Platonic soul (psuche) is different from consciousness. Actually, Philolaus (first Pythagorean to write a book) said that conscious feelings come from the combination of the mathematical soul with the body. So, Pythagorean soul can be viewed as the set of logical or conceptual forms— which constitute a person, yet can also be passed on from person to person. That’s a very different kind of reincarnation…!