Quote 1
Cole's father sat up taller in his chair. "I'm William Matthews," he announced importantly. "I'm here to make sure my son never causes problems again." He turned and glared at Cole. "This is all going to end now." (4.40)
Instead of being supportive or thinking of ways that he can help Cole, Mr. Matthews just wants to force his son to stop acting out because he's embarrassed by his behavior. He's not actually worried about his emotional well-being.
Quote 2
"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 gets super upset when his father speaks during the Circle Justice meeting because he acts like he's been the best parent ever. Cole knows this is far from the truth—he's actually an abusive, alcoholic parent.
Quote 3
Cole's father turned around to face her. "You mind your own business or I'll use this thing on you." (6.49-50)
Cole hasn't pulled his violent ways out of thin air. The reason that he sees violence as the only option is because he's grown up in an abusive household—his father beats him up, so he beats other people up.