I think there is plenty of logic in alcoholism. I want to feel good. Drinking makes me feel good. Therefore I drink. Seems logical to me.
As far as AA is concerned, it provides a framework for living your life. Once you put down the drink, it is gone. Now you have to put your life back together and live without the booze. Not an easy task, especially for many who have drank for so long we don't know how.
AVRT, to me, is just about quitting drinking. Just, bam, remove the alcohol. That's it.
I haven't really looked into other methods. For me, quitting drinking is just the start. I need more, which is why I go to AA, even though I don't like everything about it. But I've learned I don't have to like all of it. Just keep coming back, more will be revealed, that's what they say. If I want to stay sober, I have to believe that.