The issue for me isn't pulling for 2 teams, it's pulling for one team in football and another in basketball. Because in my experiences, 99% of the time the person does it because the school they root for in football isn't very good in basketball.
As a UT and KU fan, I can tell you that my allegiance to UT was formed through my parents (both alums, as well as my Dad's 9 siblings), and my allegiance to KU was formed through being 25 minutes from the Phog.
My Dad took me to KU basketball games because they were KU basketball games and it is a hell of an experience. And, I got into it, and loved KU basketball. I never went to a KU football game until I was in high school, because we spent Saturdays in the fall watching UT play, or making trips to Knoxville and Oak Ridge to go to games. KU football was never a thought growing up (and, it is still hardly a thought to anyone in Lawrence). UT basketball was never on TV in Kansas in the 80s and 90s (aside from a few Allan Houston games), and my Dad never thought making a trip to Knoxville to see a basketball was worth the money. By the way, that KU game I finally went to in high school...felt like an oversized high school game and a sideshow compared to the games I had already been to at Neyland. And, as much as you might hate to hear this, UT basketball games in TBA...well, they feel pretty ridiculous as well when compared to a childhood spent going to games in the Phog.
Were I just in it for the "good team in this sport" and "good team in that sport", I would have hopped off the UT football wagon by now; as would many others in here that get accused of being this type of fan because they are big UNC basketball fans.