First of all, Jack believes (and says so) from the beginning that he thinks he should be chief. He believes the Hunters are most beneficial to the group because they get meat for everyone, and since he is head of the Hunters, that he is naturally the best.
He felt he and his hunters were too good to tend the fire, so they let it go out as they were off trying to kill pigs.
He also puts others down (especially Piggy) through name calling and violence. Bullies often pick on those they feel are inferior to them.
He sets himself up as a king of sorts in a fortress on the rocky side of the island and keeps the others in line through beatings.
But, I think, the ultimate "better than you" move is when he actually treated Ralph like an animal and "sharpened a stick at both ends" to eventually put Ralph's head on it as an offering to the beast.