self-righteousness of those who hate BYU?
I don't think it's right to say that hating leads to self-righteousness and therefore BYU fans are self-righteous because they hate.
Self-righteous arrogance comes from pride, not from hating. Hating is a prideful response to the self-righteousness of others. In this way, BYU and Utah fans are no different whatsoever.
Or are you convinced that "yes, all fan bases have it, but BYU is worse"?