Oh, I feel so much better. So so so much better. I think he's a little befuddled; he says it came out of the blue for him. But we talked about my recent drinking history, and after about twenty minutes of that, I think he was convinced.
One interesting thing that he asked me: He said, "What is my role in this? Am I supposed to discourage you from drinking, or let you do whatever you want?" (He says I tend to throw myself into things and then decide a few weeks later to abandon that ... he says he can see us joking around in a few years about "that time you thought you were an alcoholic.") I said I honestly don't know what to tell him, but will give it some thought. For now, he says he's going to just wait it out and see if I still think I'm an alcoholic in a few months.
Thanks, everyone, for the encouragement to talk to him. I'm glad I did it, of course.