What you described for that Hatter are severe traumas that changed him. I dont know who that Hatter is, but in the case of murder's who murder based on trauma's that happened in there past, that is something that changed them and there personality.
People with abusive parents are like 90% more likely to abuse there own kids, because that is a trauma that happened to them as a child, and that is the coping strategics they are taught by example. There was a study we learned about in my psych class in which they took abusive men and asked about there childhood, almost all were abused themselves. Then they did a study of those abused as children and the majority of them abused there own children the ones that didn't had to work very very very hard to maintain control of themselves. Which took extreme will power.
In my opinion, bullying itself isnt a trait but that evil inside, that feeling that you need to put others down to make yourself feel better, or that slight sociopathic need to torment others, is a trait of personality. Whatever caused those traits might have been from trauma itself. But i still believe its a part of a person.
In TAJ, Matty is one of those people. His dad abused him severely after his mother died, and he grew up into the bully he was. But then the trauma of Nesia, showed him how he could be different. So he changed himself... and was forced to change himself, through great effort. And even in the following books he still struggles with those old tendencies of evil and abuse.