I think he's temp checking. He knows you made yourself vulnerable, he knows you were putting yourself out there, and he's afraid that he blew it. So he's making sure you're still on the hook. And he's scared he pushed you too far or rejected you too much. Now might be the time to respond honestly and let him know that yes, you are disappointed by his behaviour and you're considering your best options as to how to do forward and would like some space and time to do that.
Have you done much reading about alcoholism, Dilly? I have it in my family which is why I feel comfy speaking to it on your thread. It might not apply, and might not be useful to you - but one of the things that is often said is that it is a family illness - enabled by immediate family and damaging family as much as the addict. The family need recovery as much as the addict does.
Apparently someone with a problematic relationship to a substance or activity can't really have an intimate relationship - their primary relationship is with their substance or activity (gambling, sex, crack, work, porn - whatever - booze will probably kill you quicker than most of the other substances or activities but the way it works is pretty much the same.) They also say that the person who wants the intimate relationship with the addict probably doesn't really want an intimate relationship - they'd choose someone available if that was the case - and in the end they have a relationship with the substance at second hand, which is also called co-dependency or enabling.
I know it all sounds a bit weird - but in my experience it really is like this. My father was a drinker, and I've had to address a lot of this in my IC and it still shows up in my way of relating to other people - particularly men - even if they aren't drinkers - so it can be really deep rooted.
It's interesting your H says he's an alcoholic. There's such a huge stigma about that that people very rarely use it as a self-deprecating joke unless they secretly do mean it, or are trying to evade responsibility for their behaviour (aka: 'it's not my fault I was mean to you - I'm just an alcoholic, what do you expect?')
