Hi BD, welcome to the SR. It's good that you and your AH (alcoholic/addict husband) are seeing a counsellor and that she's raised the topic of his drinking.
You've told us what she's said about the damage it's doing to your marriage, but what about you? How does it affect you?
You seem to have a fundamentally loving marriage, but he's using guilt threats to protect his drinking, while admitting he has a problem. So your therapist is probably right that he's not ready to give up drinking yet. Maybe with further counselling he'll eventually get there. How do you feel about the next few years with him going down the same path, or even getting worse?
In the end, you can only control your own actions. You can seek support from SR and Al-anon, and read as much as you can about alcoholism. You can also refuse to enable his drinking in any way and let him feel the consequences.
I'm sure others will be along soon to tell you about how their experiences.