You said you've known him only a short time, the way he's acting is upsetting you, so it really doesn't matter if he's an alcoholic or not, does it? Why are you so determined to stay in this relationship? Especially since you've been through this drill already--and not that long ago. Why sign up for another round of unpleasantness?
Why not just tell him, "You're right, it isn't affecting me because I'm done. Best of luck, take care."