One reason why the disease model doesn't seem to fit alcoholism is that alcoholism manifests itself so strongly in the area of interpersonal functioning, in a way that diabetes or other disease do not. When I look at the questions people ask about alcoholics in their lives, it's almost always interpersonal behaviors that come up - lying, denial, outbursts of anger, etc. You don't see that on support boards for other diseases (the only exception that comes to mind in Alzheimer's or dementia - but I think dementia is broadly understood as a condition that is not of the afflicted person's making). The deficits in interpersonal functioning are almost a defining characteristic of the disease, and they wreak havoc on the people who are not "sick".
Alcoholism to me almost seems like a behavior disorder, like oppositional defiant disorder or hyperactivity in kids. Because alcoholism can be treated (if not cured) and because most alcoholics are not children or seniors with diminished mental capacity, it's maddening when they don't choose treatment, in a way that similar bad choices by people with Alzheimers or children with ODD are not (quite as) maddening.
With my ex, if he had simply consumed quarts of alcohol every day sitting by himself in the garage, even if he developed a physical dependence, as long as his interpersonal functioning was intact, his drinking would be a physiological problem, not a social one. Unfortunately, excessive drinking seems to almost inevitably be manifested by interpersonal deficits, and that's why I remain angry at my ex in a way that I would probably not be angry if he had, say, MS.