You don't ha e to leave him unless he is verbally, physically or sexually abusive. However, he has to be willing to work on his anger by seeking therapy or something like that. His anger is a personal thing and he has to be the one to find coping skill and to deal with it.

You haven't specified if he is willing to seek therapy or not but if he is struggling with anger to the extent that it seems. It's likely his best bet is to seek out therapy to deal with the core of it.