Patterson fired the SID who was considered one of the best in college athletics, and was Strong's most trusted resource at Texas. He made ridiculous rules about how often the coaches could go to the dinning halls to meet with their players, and if they went more than the allotted times Patterson put in place, they would have to pay to get in. Then the cherry on top of the Patterson shit sundae, he straight up lied to Strong about the reasoning as to why he was going to move the academic support for the football team. (He relayed to Strong that it was the President's idea, but whoops, turns out it was Patterson's idea and he just lied about that)

Here's a pretty detailed report about the events leading up to Patterson's firing: http://www.scout.com/college/texas/story/1587506-ut-president-too-much-risk-in-keeping-ad

(cliff notes version: Patterson is a shithead, and no one liked him)