What convinced me was that I kept having the same thoughts periodically ... "I think I'm probably drinking too much, I might be addicted, someday I might have to quit". But "someday" never seemed to arrive ... I didn't feel like quittting.
Then I somehow realized that "someday" was never going to just arrive ... nothing changes in addiction, it just goes on. I was going to have to just decide that it was time. I committed myself to change despite the fact that I didn't "feel committed".
Another way of thinking of it was that I was of two minds ... part of me wanted to quit, and part of me wanted to drink. I decided to side with the part that wanted to quit, rather than waiting for both parts to agree ... because they never would.