From what I've seen so far, Edelgard falls hard for Byleth. There's a scene where your character falls unconscious, so Edelgard decides to carry you back – but only if you're playing as female Byleth. Make what you will of that.

I like to imagine an El that was mostly focused on assassinations and ambition and ideology and then hot teacher shows up and she's like "oh yeah, boobs are pretty nice too."