Rivalries like UF-Tenn often were spawned from a period a few decades back where both were good. If you go back further you can find they rarely played when it was a Big Game.
That doesn't mean the rivalry is not "real", just that it's more recent than some like UGA-Auburn. But if you swap out UK for example for UF for Tennessee, you have to juggle UK to be someone else's rival for whatever reason. Then it ripples. There really are only a handful of "real rivalries" in the SEC.