Underneath any addiction can be a lot of shame. Whether that's an addiction to food, heroin or gambling. When you live with shame for years, when you berate yourself constantly it can certainly do a job on your self esteem, so he's probably right that it would be a solid goal.
You probably don't really know why he drinks, it may not even be something he understands yet.
You are powerless over his addiction. I know you know that logically but probably are still struggling with it emotionally? I think that's pretty normal, it's early days and you are really hurt.
It may be best to let him know you would prefer not to discuss it. Say what you mean just don't say it mean? Him discussing it with you at this point probably just causes resentment.
Hang in there.