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Actually in the Symposium it is Aristophanes who tells this story, as a deliberately funny and absurd way of explaining how crazy love is. It features both heterosexual and homosexual couples (these are just halves of four-legged creatures that were male/female or male/male or female/female respectively). The real argument of the Symposium is that Alcibiades' love for Socrates leads him towards the true good, which is philosophy.