Cole's father has always been a negative influence in his life. He's the reason Cole is so angry, since he's been abused and belittled by this man throughout his childhood. Mr. Matthews just cares about how he looks to other people, which is why he buys Cole plenty of expensive things in order to appear like a good father. But when he claims his devotion during a Circle Justice meeting, Cole loses it:
It was the next voice that made Cole explode. His father held the feather, toying with it in his fingers. "We've always wanted the best for Cole," he said. "His mother and I have devoted our lives to him, but he—"
"That's bull!" Cole shouted suddenly, although he wasn't holding the feather. "You drink until you can't stand up, and you're gone all the time. A devoted parent doesn't whip his kid until a shirt can't hide all the bruises!" (5.27-28)
Cole's understandably pretty angry with Mr. Matthews for lying about his status as a good father when he's really an abusive jerk. Over time, however, Cole realizes that his father will probably never change. Even when he's arrested for child abuse, he just has his lawyer get him out, never even apologizing to his ex-wife or child. He's going to continue being an abusive, unrepentant man, and for his own sake, Cole has to forgive him and move on.