Earlier in the novel the children were still constrained by the rules and regulations of society. They were trying to order themselves much in the way they had seen the adults in their world do so. In the early chapters their focus was upon survival and the chanting of kill the pig represented this survival mode. They were seeing the pig as a challenge to be overcome. As their society advanced into a unique society they were creating religion. As their religion the pig and the chant become central rituals. These rituals influence their descent into savagery.
The beast is starting to represent their human nature. They now have several new beliefs and these new beliefs are taking over. They are trying to kill, in part, the humanity from which they came.
The fear they have been living under is also a large influence. Because they have been living under the fear of the beast for a large period of time, the idea of killing it becomes tantamount to their survival.