This is a good question.
From one point of view, Piggy is an outsider in the group. He is intelligent, logical, but he lacks social skills and leadership. The boys do not accept him. Jack, on the other hand, possesses leadership skills and a desire for exploration and danger. Just from these points, we can see that the boys will not like each other at all.
Jack gains more power as the leader of the hunters and he begins to pick on Piggy. At one point he even steals his glasses.
On a deeper level, the two boys represent two different parts of humanity. Piggy represents civilization and logic and Jack represents savagery and our baser natures. Therefore, these aspects of our humanity are always in conflict. As the story progresses, Jack takes over. Piggy actually dies. This means that Golding had a dark and pessimistic view of humanity. Piggy and Jack tolerated each other but in the end they could not coexist.