I don't see why people like them. Sure they're underdogs and all that in football, but I have no sympathy for them. They want to pretend they are above sports, and they're above the rest of the league. That's fine. You deserve to lose all the time if that's the attitude you want to take.
Unfortunately my team has found a way to lose to them too much, but I still think their fans deserve to lose more than any fanbase out there, since they're so much better than caring about sports.
ETA: I didn't vote in the poll, but no matter which division you're in, you couldn't have your favorite SEC team outside of your school be anyone in your division. I wouldn't understand that. Familiarity breeds contempt, and any team you play every year in football, twice a year in basketball, and every year in baseball should trump the teams that rotate off occasionally for football and baseball and the teams you only play once a year in basketball in terms of your hate level.
If I had to vote for a 2nd favorite SEC team, it would definitely be an East team, and it would have to be one that's far away from people I interact with. I don't like Florida because I don't think their people fit in with the SEC type of fans, much like Arkansas to me. I can't do Vandy (reason above). I can't do UT. I live too close to them. Therefore, that leaves Kentucky, South Carolina, and Georgia. I hate Kentucky because I hate any school that thinks football isn't the most important sport. That leaves South Carolina and Georgia, so I guess those two are about equal for me in terms of which one I have the least hate for out of the rest of the SEC.
I wouldn't say any of them are my favorite team outside of my own, but they're my least hated.