Why does Jack say, "I'm not going to play any longer. Not with you." in Chapter 8 of Lord of the Flies?

In Chapter Eight of Lord of the Flies, Jack demands a vote amongst the boys with the intent of removing Ralpg as their leader and taking over. Unfortunately for Jack, not one of the boys votes for Ralph's removal. As a result, Jack is humiliated and is brought to tears before saying, "I'm not going to play any longer. Not with you." This one phrase illustrates Jack's immaturity and inability to cope when he doesn't get his way.