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Jack made that statement when his call for a vote of no confidence in Ralph's leadership was ignored by the rest of the boys.
they went after the beast but jack decide to forget the beast and play rolling rock
Jack accuses Ralph of not being fit to be the leader and asks the boys if they want Jack fired as chief, but no one responds to him. He runs off crying and saying that he is no longer going to be part of Ralph's group.
Well you could take his word for it. In chapter 8: Gift for the Darkness just before Jack walked away from the meeting he said, and I quote... "I'm not going to play any longer. Not with you."
After Ralph, Jack and Riger returned from seeing the "beast" on top of the mountain Jack called a meeting and accused Ralph of calling his hunters cowards which was a lie. He then held the conch against his chest and asked, "Who thinks Ralph oughtn't to be chief?" The assembled boys remained silent and Jack asked again, "Hand's up... Whoever wants Ralph not to be chief?" the silence continued until Jack eventually put the conch carefully down and left, saying "I'm not going to play any longer. Not with you. I'm not going to be part of Ralph's lot___" So the simple answer to your question is that Jack called for a vote of no confidence in Ralph and lost.