The most obvious example of such an incident in this chapter is when Jack fails in his attempt to overthrow Ralph as leader. When he doesn't get his way there, he pretty much resorts to the "I'm going to take my ball and go home" response.
During the meeting, Jack asks for a vote on whether to throw Ralph out of "office." No one votes "yes." So first, he starts to cry. Then he says "I'm not going to play any longer. Not with you." He says he won't be in Ralph's "lot" anymore and runs away.
This episode shows that Jack is not able to deal with it when he doesn't get his way -- he is quite immature and selfish.
In Chapter 8 of the novel Lord of the Flies by William Golding, there are discussions about who is to be chief. Both Jack and Ralph are contenders. Jack suggests observations about Ralph that suggest he would not be a good leader (he is a coward, he talks like Piggy, he's not a real chief and so on.) He begins to falter, reading the faces and body language of the other boys. Eventually, his voice tails off and he begins to feel embarrassed and humiliated as he realises he won't win. Instead of being magnanimous in defeat and collaborating to join forces to get off the island, he puts himself first. Hot angry tears pour down his face, and he runs off in a tantrum - saying that anyone who wants to hunt could come too.
In Chapter 8 of the book Lord of the Flies Jack has already begunto feel competition with Ralph. He resists the leadership of Ralph. He grabs the conch and calls the assembly. Ralph grabbed the conch from Jack. Jack interrupted Ralph and lets him know that he called the meeting, and he needed to be able to talk. He then tells the group about the beast. He is getting agitated by the resistance and statements of the others. He tells them to shut-up.
Ralph tires to speak stating he had the conch, but Jack is getting more frustrated and angry. He accuses Ralph of being like Piggy and tells the group that he is not a good chief. He will not let Ralph have the conch. He calls Ralph a coward.
Jack calls for another vote in an effort to remove Ralph from his role as chief. When no one responds he gets embarrassed.
"He licked his lips and turned his head at an angle, so that his gaze avoided the embarrassment of linking with another's eye."(127)
Jack gets fed up, and states he is going from the group and anyone who wants may join him.
"Jack turned and looked back at Ralph. For a moment he paused and then cried out, high pitched, enraged. --No!"(127)