Angelacress (above) has very articulately brought out the major events leading up to the rift between Ralph and Jack. What is especially interesting is Jack's choice of words: "I'm not going to play any more." To Jack, and apparently to the majority of the boys, being stranded has become something of a game, whereas to Ralph it has always been about being rescued. Being rescued isn't "fun." Hunting pigs is fun; feasting is fun; dancing is fun; and - ultimately - killing is fun."
Ironically, most of what Jack says about Ralph is true. He's a "good" leader, but not an effective one. The draw of Jack's skill at speech, his bravery, and his charismatic personality are too much for Ralph, and given the opportunity, the boys slink off to join the tribe of the hunters.
In chapter 8, at a meeting called by Jack, Jack accuses Ralph of being like Piggy and of being a poor leader. He tells them Ralph is a coward as well, and that he ran from the beast while he and Roger stayed behind and faced it. He tells them Ralph is “not a hunter. He’d never have got us meat. He isn’t a prefect and we don’t know anything about him. He just gives orders and expects people to obey for nothing.” Finally Jack asks them to vote again to see if Ralph should not be chief.
No one moves. He asks again but the boys remain silent. Angry, and with tears of humiliation in his eyes, Jack lays the conch at Ralph’s feet. “I’m not going to play any longer. Not with you.” He asks those who wish to hunt to join him and then walks off.
This split is a result of growing tensions between Jack and Ralph. Ralph has continued to try and remain civilized, though life has gotten harder and harder for the boys stranded on the island, left to fend for themselves. Meanwhile, Jack has become more and more savage, concerned primarily with hunting and killing. The two boys disagree about major ideas on how the island should be run and how thier population should be governed. As a result of these differences, the argument and resulting schism in chapter 8 was inevitable.