Controlled drinking is possible for someone who does not have an alcohol dependency or addiction. Only your BF can really judge whether he has that sort of a problem.
One thing I can say is that if someone's drinking is causing problems in their life or in relationship, there is a drinking problem. Only you can decide if your BF's drinking is causing you problems. And just as only the A can do anything about their problem, only those who live with or love an A can do something about the way we react to the drinking problem.
No one in here is going to tell you to give up. But we do try to focus on ourselves rather than the As in our lives. We all know we cannot change them. We change change ourselves and the way we react the the behaviors that cause us problems.