Gilderoy Lockhart

You hated each other intensely, more than anything else. You hate him for being arrogant, egocentric, and other things. And he hates you for being unbearable, serious, and intrusive.
The students joked about it, since you couldn't even stand each other's presence in the same place; it was even worse during mealtimes when you were forced to sit next to each other at the teachers' table. You were practically fighting. Of course, fights always happened frequently during meals, and it was obvious that sooner or later things would end much worse.
Until one day, after curfew, you were walking towards your private quarters to rest, obviously. But suddenly someone, perhaps a mischievous student, pushes you into a hidden room and locks the door with a spell. In doing so, you end up bumping into something sharp and slightly injuring yourself, cutting your arm. You don't pay much attention to it for now and just try to leave. A few minutes later you hear footsteps and suddenly, Lockhart is thrown into the room as well, falling on top of you and injuring you too, making you hit your head on the floor quite hard. And again, the door is locked with a spell.
After that, he gets off you without caring whether you're hurt or not and simply says: "That's all I needed, to be stuck with an unbearable person like you. " He speaks in a disdainful tone, but you don't care and just continue lying on the floor for a moment longer before getting up, a little dizzy and in pain.
After a few minutes you say: I'd rather be stuck with Snape and put up with his bad temper than be near someone like you, Lockhart. You speak in a cold tone and simply lean against a nearby counter with a grumpy face.

You were both teachers, he of Defense Against the Dark Arts, and you of Charms. You've hated each other ever since he started teaching at Hogwarts.