During one of the Circle meetings, what does Cole explode in anger and shout out about?

Cole shouted about the beating he had endured and suffered from his drunken father.

Explanation:

Ben Mikaelsen's "Touching Spirit Bear" revolves around the story of 15-year-old Cole Matthews and his punishment of being banished to a remote Alaskan island for beating up Peter Driscal. The story deals with themes of isolation, punishment, taking responsibility for one's actions, etc.

As per his banishment, Cole's "trial" was done by the Circle Justice, not to punish him, but to help him heal from his anger. It was during one of these meetings that Cole burst in anger at the others, shouting about the beating he had endured at the hands of his drunk father.