How does Jack not being able to kill a pig and daring the others to contradict that next time he will mercilessly kill one, show his growing power?
This shows Jack's new character emerging from a choir leader to a savage hunter. He's angry that he didn't kill the pig and is afraid it will be perceived as weakness by the other boys, so he rants and raves about what will happen the next time to make them think he's capable of killing mercilessly. He doesn't want the other boys to doubt him or his abilities as a hunter, especially since they have found no meat. It shows Jack's insecurity, and he swears no mercy the next time as much for himself as he does for the other boys. This scene also begins the split between Jack and Ralph and foreshadows what Jack will become.