the cats represent boys.
So you've got this handful of girls who are all pretty normal for the most part, and sasaki in particular is tall and hot. but they never talk about boys. No crushes, no dates, not even blowing them off. There was a boy during the first season, but he was basically written out of the show. and the teacher's creepiness was ratcheted way down to him just being weird.
sakaki's trials and tribulations with cats are analagous to a young girl discovering boys, being burned by a first love, and finally meeting a nice guy from out of town who respects her and protects her. or maybe she discovers that she's a lesbian. that makes sense too, now that I think of it.
that's just like my opinion, of course. but somebody brought it up a while back and I think the theory has legs.
I haven't been on /azu/ in while and I recently shared this theory in another thread. One of the more interesting things that I think I originally picked up from here...