Oh, I know it can be sooooo frustrating. There really is no way to 'convince' him he's wrong. You are trying to have a rational conversation with an irrational active alcoholic. There is no way that can happen.
One of the other Mods here has a great saying in her signature line, and it took me a while to appreciate it. It says "What other people think of me is none of my business." Remember, he can say or think whatever he wants, but it doesn't make it true