Symposium: series of speeches about love, then Alcibiades' speech about Socrates. Phaedrus takes love as a god; then idea of two gods (lower love--desire--and heavenly love--loyalty). Then love as a cosmic force (love as an effect on the human body.)
Aristophanes' story by way of myth: the story of humans as pairs, split to stop them challenging the gods. So desire for reunion is desire to reunite with missing half. The serious point: love as desire for a strong kind of union, i.e. an identity.
Socrates rejects previous ideas. Diotema, his imaginary interlocutor, takes love as desire. So if love a god, he's desirous, and therefore doesn't have a lot--he's a poor, rough god. So that looks like what Aristophanes said--love a desire. But Diotema says that the object of desire can't be something that is a proper part of me, or possessed by me--it must be something that I think of as good, i.e. the beautiful.
But now, as usual: if want what's beautiful, should not be content with physical bodies--should seek the Form of beauty. Get explanation of desire for children this way: attempt to imitate immortality of the Form of beauty.
Love always points towards Form, so away from body and towards soul--so love is expressed as a desire to make soul beautiful, i.e. to educate. So qualified approval for the troubling practice. A higher expression of this kind of love: laws that improve many souls, not just one.
But highest of all is grasping of the Form itself: i.e. philosophy.
Image of souls as winged chariot: the noble horse and wild one, steered by charioteer. If well steered, can glimpse forms. If not, don't. Note similarity of this image to the tripartite image of soul in The Republic.
The present point? Seeing a beautiful person reminds us of the realm of Forms. Note this like the theory of recollection of Forms from the Phaedo. So a relationship, if it goes well, leads to a philia kind of relationship, not an eros kind.
Objections: this is a weird picture of love. If beautiful persons' role is to remind us of the Form of beauty, any beautiful person will do as well. It seems the person him/herself drops out of the picture. That seems to miss something important about loving relationships.