Quote: You don't have to hate each other for it to be a rivalry. There's lots of rivalries based on mutual respect.
In sports, I think hate is usually a form of respect, even if you don't want to admit it.
I actually grew up in Louisville, and was the biggest Louisville fan in history. I've since gone to another college for undergrad, yet another college for grad school, and have worked at and or lived in several places since then so my loyalty has faded toward Louisville as it has grown for other schools. I like to see them do well, but I wouldn't call myself a fan.
But when I was a fan, Cincinnati was not a rivalry. At the very least it didn't fit my definition of a rivalry. It was oftentimes a big game, but it didn't move the needle nearly as much as Memphis or Kentucky did. Not even close. Even in the late 90s/early 00s under Huggins when Cincinnati was clearly the better team, it was still a big showcase game, but not a rivalry.
Even in the Big East years, I think there was more heat between Louisville and West Virginia than there was between Louisville and Cincinnati.
That's not an insult to UC. Sometimes you just don't hate everybody. If anything, I think Louisville fans rooted for Cincinnati far more often than they rooted against them.