I never liked sports until I began living with my wife. She likes sports, but is not an extreme fan of a particular team. I learned from her that it is possible to pretend to care about the outcome of events in the game and enjoy the experience.
I do think there is something different about the way I like sports than the way a real fan does, but I can appreciate the talent of the best players teams and enjoy pretending to care about points and so on. In order to do that, you have to learn enough of the basics of the game to have a sense of what is going on. Once you can see an attack forming up and then succeeding or being beaten by a well executed defense, you can then pretend to be a partisan for one side for the duration of the game.
Using this method, I am able to join my wife in watching American football games, basketball games, baseball games and football/soccer.
I have always enjoyed watching some of the olympic sports like high diving, long ski jump, rowing, sprinting, biathlon, biking, marathon, etc. This is less team oriented and more appreciating the pure physical prowess of the individual athletes.
This is very much the same way that I enjoy a lot of modern dance. I don't think I have much of an appreciation for the more complicated aesthetic aspects of it, but I enjoy the dancers' amazing skills and the pattern and basic visual design.