AA and others have caused a lot of unnecessary mischief over the years by appropriating a term that has a long history of application to physical afflictions only. Even the use of the term "disease" in the wider world of mental illness is problematic. A disease, strictly speaking, is something like cancer, or the aforementioned chicken pox. The complex psychological syndrome of alcoholism may include disease like physical symptoms, especially in its latter stages, but it's primarily mental, i.e., an affliction of the brain, the most complicated known organ in the universe, and therefore far more intractable to treatment.
The real problem arises which individual brain users, i.e., alcoholics, use the term "disease" to sort of absolve themselves from participation in and responsibility for their own lives, as if a foreign virus entered their body and attacked their immune system. While it's true that the compulsion to drink becomes almost irresistable for alcoholics, the complex factors that go into that tortured compulsion are chiefly psychological, and not comparable to a virus.
And don't even get me started on all the "alcoholism is genetic" drivel so often bandied about by the substance abuse community, a community with extensive vested interests in the spread of all this inaccurate terminology.
Whatever you call it, it's fatal. So argue, debate, whatever...