Jack hates all authority. He's the trouble maker for whoever is in charge. When Ralph is voted chief, the only way Jack is able to save face is to become the head of the hunters. He craves power. If you remember, the first time we see Jack, he is leading the choir boys. From the beginning he is able to control others in a way that Ralph cannot. Symbolically, Jack represents the id, the part of the human psyche that lives in the here and now, who wants instant gratification, and who resists control and discipline. We see this characterization throughout the novel with Jack's focus on fun and games rather than long-term goals of shelter and rescue. As Piggy astutely tells Ralph, "He hates you."
To me, the most likely reason is that he was simply ambitious. I think that he thought that he was the person who was best qualified to lead the kids on the island.
I think that part of this is because he was such big shot at the school he had attended in England. He was the head of the choir and he was Head Boy. Both of these were positions of great importance.
So Jack basically thinks that he is better than Ralph and he thinks he ought to be the leader.