Am I trying to fix something that can't be fixed?

I have been dating my current boyfriend on and off for about 2 years. I really care about him but sometimes his actions scare me. He shoved me once when he was drunk. I've seen him get really angry when he was intoxicated and has tried to start numerous fights over petty things.

He also tells me that he doesn't like to talk about serious things with me and tells me I'm too serious all of the time and it's stupid. He gets angry with me because I don't talk to him all day long. The other day he got drunk and called me and told me that I was the problem in our relationship.

Every time I try to talk to him about his anger he gets upset and refuses to talk about it. He also gets angry if I'm around my friends and I am talking to him. He knows he has anger issues but says he can fix them by himself.

I don't know if this is a healthy situation for myself or if I should try and work through our issues and help him with his anger problems.