I've had a few people tell me they don't think I'm an alcoholic. I just say that it doesn't matter what the label is, alcohol was doing me no favors, causing me lots of problems, and that I choose not to drink anymore. I don't actually care if I'm an alcoholic or not. Because now I live a sober life, and I greatly prefer it.
I think people don't understand why someone would willingly give up drinking if they aren't "actually" an alcoholic. Well, there are a lot more reasons for me to give up drinking than there are to continue. That's all that matters to me.