pigeon hole. There are a great deal of reasons and situations why LDS choose not to be a fan, or as you say "hate" BYU athletics.
I am new to the board, but always lurking. I am a Ute grad and fan. I was raised LDS by goodly parents in Southern California but was more of a UCLA fan than any other team. I attended BYU for a year following my mission. I did not care for the experience and chose to transfer to the U. I have no regrets, and enjoyed my experience at the U to the point that I am still a big supporter of the school, the athletic program, etc.
Everyone comes from different situations, and walks of life. Many, many LDS were not raised as BYU fans. Due to the nature of sports and rivalries (Utah, Utah State especially), it's easy to see where "hate" gets thrown into the mix.