Why did Cole burn his shelter and supplies? What did he think the ingredients of his cake were?

Cole planned on escaping the island. He burns the shelter and supplies out of rebellion against authority. Cole still lives inside his anger and his pain. He says his drunk father beating him up and his drunk mother watching are the ingredients of his cake. Both ideas have a destructive, futile, and dark element to them. There is no sense of hope or growth, only destruction.