Considering your descriptions of your AH's behavior over time, I think the alcoholic vs. problem drinker issue is a moot point.
Also, the reason the therapist resists the label alcoholic is usually a treatment decision. I heard somewhere, maybe on here, that one of the first things they train addiction counselors is not to confront addicts with their addiction because it almost always closes the avenue for treatment.
Emotionally, I think you might just be looking for an easy way out. I get it -- I've been doing it lately too. But when we minimize the adverse effects of our partners' choices -- for whatever mental health reason -- we're selling ourselves short. What I've learned is that this is a dysfunctional way of achieving "stability," and that true stability is hard won, and a process -- not something "achieved" -- and usually involves making different decisions than the ones I'm hard wired to make.