For those of you unfamiliar with Utah universities, there exists a significant rivalry between the University of Utah and Brigham Young University. If you did not know this rivalry existed then you might have even mistaken the two schools for being the same entity or of the same type.
That is probably one of the many things that fuels the fire. It has been my experience that the rivalry is actually one-sided. While BYU sees it as a fun (sometimes intense) competition, people at the U often let it decay into complete hatred. I am not sure why this is.