As someone who used to be a sports-hating girly girl who came around, perhaps I can give a bit of perspective.
Sports serve several psychological purposes. First of all, they tie people together, creating a much needed sense of community that is lacking in our modern world. Second, they serve much the same purposes as the reading of many novels--creating heroes and villains that help us learn about ourselves and others through stories, or helps to fill an unfulfilled longing. There is even a willing suspension of disbelief involved in order to invest one's self in the narratives, which partly explains some of the irrationality of sports that leads its followers to be called fans (a.k.a. fanatics).