This is true. However I have potential ideas!! See if there's something you like?

>They were briefly friends during that period when Kira was being rebellious shit?
>Kira caught Katou tormenting an underclassman and, uhm, given him a black eye for it.
>They have some kind of competitive rivalry through video games (they may or may not know who's on the other end of the handle).
>One of Katou's girlfriends dumped him for Kira.
>Fellow classmates; a teacher has foisted Kira onto Katou as a semi-willing tutor.