How I read that quote is more along the lines of:
"I am an A, and I know I put my loved ones through a lot."
"Now, there are A's in my life that I am having to deal with"
"I wonder if I'm having to deal with these people is some sort of cosmic retribution for what I did to others while I was drinking."
Not, "I became an A after dealing with one."
That said, many children who grow up in an alcoholic household have a higher likeliehood of becoming alcoholic themselves.