Well, they both were fighting since childhood, remember? Like two dominant wolves in a pack. They both felt threatened, obviously with reasons. At the end, she challenged him and lose. At this moment, Two-Spear could have killed her but he didn't. I am not sure Skyfire would have done the same. He chose to let his elf side take control then, he chose to leave where he could have been Wolf Alpha. That is a reason not to blame him too much.
I don't like the way he treated Skyfire, but I also don't like the way she acted. She was indeed proud, but selfish-proud. She too wanted the tribe to be protected, and indeed she saw Two-Spear's leadership could endanger it. But above all, she assumed she was best fitted to be chief only because she was born from recognition. Better than him only because of her blood? Such a way of thinking leaves a bad taste... :P