Everyone has a different way of dealing with the problems they face. Jesse doesn't know how to talk about the feelings he has. He feels neglected, angry but most of all useless. He has seen his sister suffer for years and his whole life has been warped into her sickness and medically he is unable to help her. Though nobody blames him for it, no one has told otherwise and deep down he has always felt that sense of failure.
He is also a child just craving for just a moment of his parents attention. They stopped trying to control him and then the taste of freedom was good. He doesn't have to think about anything when he is off being a fool and burning down buildings. It is his defence mechanism
All Anna has known has been trips to the hospital. She has been in hospital just as much as her sister has and it just seems like the natural thing to do. She doesn't know life any different unlike Jesse. Her nature is just to be compliant and that is how she deals with it.