mythology

One story about soulmates, presented by Aristophanes in Plato's Symposium, is that humans originally consisted of four arms, four legs, and a single head made of two faces, but Zeus feared their power and split them all in half, condemning them to spend their lives searching for the other half to complete them:

[Primeval man] could walk upright as men now do, backwards or forwards as he pleased, and he could also roll over and over at a great pace, turning on his four hands and four feet, eight in all, like tumblers going over and over with their legs in the air; this was when he wanted to run fast …Terrible was their might and strength, and the thoughts of their hearts were great, and they made an attack upon the gods ... Doubt reigned in the celestial councils. Should they kill them and annihilate the race with thunderbolts, as they had done the giants, then there would be an end of the sacrifices and worship which men offered to them; but, on the other hand, the gods could not suffer their insolence to be unrestrained. At last, after a good deal of reflection, Zeus discovered a way. He said: 'I have a plan which will humble their pride and improve their manners; men shall continue to exist, but I will cut them in two and then they will be diminished in strength and increased in numbers; this will have the advantage of making them more profitable to us. They shall walk upright on two legs, and if they continue insolent and will not be quiet, I will split them again and they shall hop about on a single leg.'
—Aristophanes, Plato’s Symposium.
Some argue that souls are literally made and/or fated to be the mates of each other, or to play certain other important roles in each other's lives.
According to Theosophy, whose claims were modified by Edgar Cayce, God created androgynous souls, equally male and female. Later theories postulate that the souls split into separate genders, perhaps because they incurred karma while playing around on the Earth, or "separation from God". Over a number of reincarnations, each half seeks the other. When all karmic debt is purged, the two will fuse back together and return to the ultimate.