This is the gist of the rest of the speech, if you'd like to read it:
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: 'Methinks I have a plan which will enfeeble their strength and so extinguish their turbulence; 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.'
He spoke and cut men in two, like a sorb-apple which is halved for pickling, or as you might divide an egg with a hair; and as he cut them one after another, he bade Apollo give the face and the half of the neck a turn in order that man might contemplate the section of himself: he would thus learn a lesson of humility. Apollo was also bidden to heal their wounds and compose their forms. So he gave a turn to the face and pulled the skin from the sides all over that which in our language is called the belly, like the purses which draw tight, and he made one mouth at the centre, which he fastened in a knot (the same which is called the navel); he also moulded the breast and took out most of the wrinkles, much as a shoemaker might smooth leather upon a last; he left a few, however, in the region of the belly and navel, as a memorial of the primeval state.
After the division the two parts of man, each desiring his other half, came together, and throwing their arms about one another, entwined in mutual embraces, longing to grow into one, they began to die from hunger and self-neglect, because they did not like to do anything apart; and when one of the halves died and the other survived, the survivor sought another mate, man or woman as we call them,--being the sections of entire men or women,--and clung to that.
Thus they were being destroyed, when Zeus in pity invented a new plan: he turned the parts of generation round to the front, for this had not been always their position, and they sowed the seed no longer as hitherto like grasshoppers in the ground, but in one another; and after the transposition the male generated in the female in order that by the mutual embraces of man and woman they might breed, and the race might continue; or if man came to man they might be satisfied, and rest, and go their ways to the business of life. So ancient is the desire of one another which is implanted in us, reuniting our original nature, seeking to make one of two, and to heal the state of man.
Each of us when separated, having one side only, like a flat fish, is but the tally-half of a man, and he is always looking for his other half. Men who are a section of that double nature which was once called androgynous are lovers of women; adulterers are generally of this breed, and also adulterous women who lust after men. The women who are a section of the woman do not care for men, but have female attachments; the female companions are of this sort. But they who are a section of the male follow the male, and while they are young, being slices of the original man, they have affection for men and embrace them, and these are the best of boys and youths, because they have the most manly nature.
Some indeed assert that they are shameless, but this is not true; for they do not act thus from any want of shame, but because they are valiant and manly, and have a manly countenance, and they embrace that which is like them. And these when they grow up become our statesmen, and these only, which is a great proof of the truth of what I am saying. When they reach manhood they are lovers of youth, and are not naturally inclined to marry or beget children,--if at all, they do so only in obedience to custom; but they are satisfied if they may be allowed to live with one another unwedded;
And such a nature is prone to love and ready to return love, always embracing that which is akin to him. And when one of them meets with his other half, the actual half of himself, whether he be a lover of youth or a lover of another sort, the pair are lost in an amazement of love and friendship and intimacy, and one will not be out of the other's sight, as I may say, even for a moment: these are the people who pass their whole lives together, and yet they could not explain what they desire of one another. For the intense yearning which each of them has towards the other does not appear to be the desire of lover's intercourse, but of something else which the soul of either evidently desires and cannot tell, and of which she has only a dark and doubtful presentiment.
Aristophanes' Speech from Plato's Symposium