I think I get what Army is saying...while one can qualify a rivalry such as a friendly rivalry...I think a necessary ingredient is the passion that mentioning the rival brings out in fans. The one who mustn't be named, like it or not (CJL), has always evoked a strong gag reflex, even when we hadnt played much football against one another or the series was very much one sided.
If I had to pinpoint the reasons for the rivalry, it most likely has to do with proximity, competing for the same resources, players, students, carry over from high school rivals etc. Growing up in Tampa I have plenty of friends and family that made the mistake (lol) of choosing the wrong Mikey mouse school.