Well, there are a couple of reasons. It all started with Squirrelflight and Ashfur being together, and then Squirrelflight starting like Brambleclaw. Ashfur got so mad, he told his clan, Thunderclan, the truth that Hollyleaf, Lionblaze, and Jayfeather were Squirrelflight's foster kits, not real kits. Hollyleaf knew Ashfur would annoumce this to all the clans at the susunod clan meeting, and that's one of the reasons why Hollyleaf killed him. Also, Hollyleaf knew that Ashfur was so jealous, that he was going to kill Hollyleaf, Lionblaze, and Jayfeather!