Plato wrote a lot about love relationships between men. Is a typical grooming tale that he was teaching to his alumni. Is easy to follow the dots here.
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.