As one who does not believe alcoholism to be a disease, I address this issue with the notion that one should feel shame for their bad decisions. There is no shame in having a drink, but there is shame in driving drunk, starting a fight, wrecking a relationship, poor performance on the job, etc. It is that shame that eventually drives many people to sobriety, or at least to making better decisions. The human conscience sits on our shoulder and tells us when we've done right or wrong. It makes us feel things such as guilt and shame. Those that don't feel those emotions are commonly referred to as sociopaths or psychopaths. That, of course, is also a debate as to whether it's a "disease", or just bad eggs, bad people. There's billions of people. Some are going to be bad and do bad things.
I also don't believe in "once a drunk, always a drunk". If I had ever had a DUI, I wouldn't tell people "Oh, I have this disease, I'm an alcoholic, you see". I would instead say "I made a really poor choice and got caught, and I'll never do that again".
I see absolutely no reason to "out" oneself as gay or alcoholic. Neither are actually conditions. One is a sexuality that is actually nobody's business, and the other is a term with a very ambiguous meaning. If you choose not to drink, it shouldn't be because you're an alcoholic, but because you're sober. People love to define others into neatly packaged groups, usually for the purposes of stereotyping, judging, or otherwise making rash decisions on their character without first knowing the person.
That's just my two cents.