In Chapter Nine of Lord of the Flies, there are two primary incidences of man versus man conflict.
First, Jack has declared himself the ruler of a new tribe, one that centers around violent bloodlust and the act of hunting. Hungry and scared, many of the boys abandon Ralph's leadership and join Jack's tribe. Thus, a man versus man conflict of leadership occurs between Jack, who has turned into a terrifying tyrant, and Ralph, who wants to maintain the carefully structured democracy.
Second, Simon has made the shocking discovery that the "beast" is really just the silhouette of the dead airmen, whose parachute lines were tangled on a group of rocks. Simon realizes that the antagonist that legitimized Jack's leadership is not real; when he goes to deliver this news to the boys, he is slaughtered in their crazed frenzy. Although the boys have mistaken Simon for the beast, they are still destroying another human being in a case of man versus man conflict.
In Chapter 9, Jack has become a self-selected king, while Ralph is trying to live on the island with some sort of dignity and righteousness. That is the main conflict of the story. However, Simon brings the conflict to a head, as he comes to the boys with information that the beast isn't real and that it is a dead pilot on top of the hill. He has the answer that should help the boys come back to a state of normalcy, but he doesn't have time to tell them because they kill him, thinking he is the beast.