In the beginning there were three parents; sun, earth and moon. From the sun came male; from earth, the female; from the moon, the androgyne. Each of them was a double, one head with two faces looking out in opposite directions and four arms and legs. They moved about on the earth with a great deal more freedom and power than humans do now.
However, one day they decided to scale Mt. Olympus to attack the gods.
The gods were angered by this. How could they show the humans the error of their ways? They had to devise a special punishment.
Eventually it was decided that humans weren't a real threat, but they needed to be taught a lesson, so Zeus proclaimed that if they were cut in half, they would be only half as fast and half as strong. He cut the children of the sun, earth and moon in half and Apollo made the necessary repairs. After the surgery, the half creatures ran around frantically looking for their other halves, seeking them out, embracing them, and trying to join together again. Unable to join, the creatures despaired and began to starve to death in their sorrow.
Zeus, worried for his worshipers, instructed Apollo to create a means to rejoin temporarily. This Apollo did by turning the genitals to the belly side of the body.
The creatures who had been double women before, naturally sought out women; those who had been androgynous, sought out members of the opposite gender; those who had been double men, sought out the company of men, and not simply for intercourse, but so they could become whole again by being rejoined with their soul mates.
(Soul Mates, from Aristophanes' Speech on Love from the Symposium by Plato, adapted by N.S. Gill and Bergrún Anna Hallsteinsdóttir)