Perhaps he is jealous of Jane and her intelligence, since he obviously does not enjoy school and had his mother take him out of it. He is also the only male in the house so maybe he is trying to prove his 'masculinity'.
John is very pampered and spoiled so this makes him think he is better than everyone else. He is use to getting his own way all the time so when Jane defies him, he is enraged and takes his anger out on Jane by hitting her. This is his way of showing Jane that he is the boss and whatever he says goes.
John might have some insecure about himself so maybe he takes his anger out on Jane. He also may be dealing with a lot himself and he does not know how to deal with his anger. So by hitting her he feels as though all his anger is gone.
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