There you have tradition, competitiveness, cockiness, and a touch of nastiness. I'm better than you, and I can prove it. I like that. It jacks you up for the big game. It means that, whenever your alma mater plays them, that IS the game of the year, the game where, regardless of whether you go to Ohio State or Alcorn State, that's the game you want to win.
Profanity is used affectionately.
The opposing fans are hostile, the referees are always biased, and the opposing team mascot is a spy. My prime example for this is Notre Dame. Growing up, I hated them. Heck, I don't know. I think it was because they were so universally loved as America's team.