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.
The entire history is basically an excuse for the old "hey, we should sleep together and have fun" (shrug). Maybe it worked fine for Plato.