why is cole so angry?

He has become a criminal, he does not feel he has had a very respectable upbringing, and he has become a victim of a kind of justice which makes no real sense to him. Going to an island to "think" does not seem to be the kind of punishment he thinks he should receive.

In Chapter One? He is angry because he has to go the the island. He's angry at the situation, the justice system, his parents, and even Peter. He blames everyone else for what he's going through, and is unable to see his own part in the events that have unfolded.