Taehyung's family situation was never good. Taehyung's father and mother left him and his sister alone. When his father came back (Taehyung was seven) he was expecting a nice faminly. However, as soon as he tried to hug his father, he was struck in the face. He was beaten so hard that he lost consciousness for a second.
Despite being hurt like this everyday, he stayed innocent. He wanted to become a superhero. As time goes on, and the beatings continue, he feels worse and worse. He likely feels it is his fault his family doesn't work. He gets more angry, and starts skipping school and picking fights. Without a father figure, he looked up to Namjoon as one. He thought whatever he said was right, and so pushed down his own thoughts. This causes them to explode out of him, often causing trouble.
He tried to stay away from home as much as possible, to stay away from his father. He started doing graffiti, getting him into trouble more often.
Still going through abuse at home, he finally is done with it. In a fit or rage at seeing his sister being hurt by his father, he breaks a bottle over his fathers head, and stabs him in the gut, killing him. He becomes afraid of his anger, though it is more likely depression, and acts on it using violence.