Roger kills Piggy because he can, and he has realized that no one on the island can or will limit his cruelty. Early on in the novel, Roger tests the boundaries of his bullying in the chapter "Painted Faces and Long Hair." He stalks little Henry down the beach, and just when Roger is sure that nobody is watching, he begins to throw pebbles at Henry, but throws to miss. The narrator comments that Roger's arm was held back by the "taboo of the old life;" and Roger still recognized the boundaries put into place by "parents and school and policemen and the law" (62).
On that fateful day at Castle Rock, Roger has lost his old inhibitions. He stands high overhead on an outlook where an extremely large boulder balances precariously while Piggy below delivers his speech on fairness and the importance of the law and rescue, all of which are ideas that Roger probably detests. Roger leans on the lever placed under the rock with "a sense of delirious abandonment," a descriptive phrase which indicates Roger's wholesale enjoyment of the deed; he derives immense pleasure out of others' suffering (180).
Actually, Roger did not throw a rock, he kills Piggy by releasing a boulder. But he does this because of his growing savagery and thirst for blood. When Roger was tempted to hit a littlun on the beach, he was impeaded by past rules and restrictions of life back in England (it is wrong to hurt others) so he relieved his tension by throwing rocks to the side of the littlun. In this, it is evident that Roger contains dark urges. So when Piggy was in proximity of the boulder, with conscience all lost, Roger kills him in cold intent.
The fight was a dispute between Piggy and the members of Jack's tribe for stealing his glasses. Yet Piggy also goes into depth about the corruptness that is happening on the island. He asks for Jack's tribe to analyze themselves and stop their evil ambitions. However, like all other speeches by Piggy, he is ignored and recieves only scorns by Jack
this was from pior knowledge, but i hope it helps!