I tend to root against the "football factories", although I like when they play each other. Within the section/conference I'll root against our main recruiting rivals but always root for them in intersectional/non conference games because our reputation is tied to theirs.
Other than that it's mostly coaches. I didn't like Woody Hayes, Barry Switzer or John McKay. I started out not liking Bear Bryant and liking Joe Paterno but those positons reversed themselves over the years as I found out more about them. I used to be amused by Lou Holtz but not these days. Bud Wilkinson is my all-time favorite. I see him as similar to John Wooden. I don't like coaches who hop from job to job, often before the job is complete, (sorry, Nick Saban and cousin Lou). I also don't like coaches who bend the rules and get in trouble or leave their former employers in trouble.
It's more about the individuals than the schools, which are what individuals make of them.