The reason the Gator fans appear to be rooting for the Vols is the same reason that most UT fans appear to root for Kentucky over Clemson. Basically, they do not see us as much of a threat and given Fulmer's dismal record over the Gators I can't say I blame them for their haughtiness.
There is absolutely no reason to support UF. First, there is NO extra shared revenue for UT if UF wins. The payout is predetermined before they ever play the game so those who have brought that up as their justification are laboring under false pretenses. Second, the strength of schedule component was removed from the BCS calculations so it's not like a UF win is going to help UT next season. While the strength of schedule may remain a factor for individual voters in the two major polls, this is the end of the season so it's not going to advance the Vol's cause one lick. Basically, the strength of schedule jusitification is a straw man.
I have also seen the esoteric notion of conference pride used for UT fans to support the Gators. When I was a kid you never heard the "S-E-C" chant at UT football games. This is something that the conference bottom feeders latched onto in order to provide some sense of self worth. The idea being that if you suck as a participant in the toughest conference, maybe you really don't suck so bad compared to other teams in other conferences. When the Vols strap 'em on and line it up they are not playing for the SEC. They are playing for UT, the state of Tennessee that suports the university, and their fans. THAT'S IT!
Finally, I've even seen a couple of posts where people seem to think that they will get some type of bragging rights if UF wins because they will be able to say that UT came within a point of beating the national champions. To me that's like saying I drew 22 on a big hand in blackjack. It's still a loss and nobody is going to care. Try tossing that 1-point line out to a Gator fan and you'll probably get hit with a comeback about Air Force.
Most of the Gator fans who visit here regualry are nice, civil folks and I'm not trying to antagonize anyone but there is no way in hades that I will ever root for the Gators unless a UF win is necessary for UT to win the SEC East and even then I'm more interested in the other team losing than I am in UF winning.