From Timaeus:
"If a man lives badly, he will be born again in the next life as a woman and if he (or she) persists in doing evil, he (or she) will become a brute, and go on through reincarnations until at last reason conquers."
A bit sexists but here East meets West.
Reminds me of a movie, Groundhog Day, where a guy wakes up to the same day, day after day. In each of his days the same basic events occur but he changes which makes his (and other's) experience of those events quite different. Throughout the story is a common thread of his realtionship with a woman, which serves as a barometer of his progress. Starting out as a happy-go-lucky self-centered obnoxious brute, once he is aware of the nature of his existence (unending without lasting consequences), he goes through a progression from full-on hedonism and exploitation, to renunciation (bhoga-tyaga), to seeking annihilation (knowing everything that was going to happen was TOTALLY boring), to altruism, to love. Once he learns to love selflessly, it is a new day. The "well-reasoned heart" conquered all lower forms of existence.
I see it as less sexist and more a commentary on how awful life was for women during that time. I can only imagine that the prospect of becoming a woman in the next life during Plato's life was very ominous. As the gender gap closes, one can either see becoming either gender in the next life as unfortunate or maybe fortunate depending on how you see it.