I think that many alcoholics see it as this: They have incredible willpower. They probably have more willpower than most people. The problem is, willpower isn't how you quit binging on alcohol or on food. Your will is the problem. That's why when they finally accept powerlessness over the problem and completely give up they're finally on the way toward recovery. I don't think everyone has to go to AA to figure this out, either. Some people can just let go and stop trying so hard and the problem just loses its grip on you.
I also agree with you Knifegill that you can be cured. They said the same stuff in Al-Anon, that you have to keep coming back forever because it's like peeling away the onion. After a year I felt completely fixed and I've never been in a relationship with another alcoholic ever again. I don't attract them anymore, either. They can't find in me the thing they need and I can't find in them the thing I need. And I no longer can attend an Al-Anon meeting and feel like I belong there. I still recommend it highly to anyone in need, but I'm just not in need anymore.
Female, 5'3", 48, Starting weight: 163lbs. Current weight: 135.
Starting bench press: 30lbs. Current bench press: 77.5lbs.