That may be true in some states, but the Ohio State/ TTUN rooting for is Very clear ...Bama people root for Aubarn to lose all the time. But a difference might be because most of the teams down here have an in-state team as their biggest rival. That leads more towards divided loyalties, as opposed to schools where the rival is someone from out-of-state, giving you no reason to root for them.
Back when I was a kid, I would root against Ga Tech (grew up in a UGA household), but then I went to Tech. Could never develop the hatred people at school had for Georgia (mostly people from out-of-state), so I just root for both (except when they play each other).
Personally, now I think it’s silly to actually hate a team, I just prefer to enjoy the game, and generally root for my favored of the two to win, not for one of them to lose.
Its one way or the other here ...
That doesn't mean everyone from Ohio roots against ichigan same goes, the other way, not everyone from Michigan roots for them either.
However, its always one way or the other.