The abuse from Cole's father has impacted him. The hitting, punching, kicking, etc have all fueled his anger. His fathers behavior impacted his future decisions and thoughts.
His mother has also caused his anger. Although she never physically hurt him, emotionally she did. She didn't protect Cole. She also drank the pain away. This caused Cole to feel not loved, and raging with anger.
Lastly, in his mind, he is alone. He feels like nobody loves him or care about him. So he takes away the pain by taking his anger out on others.