Nature, nurture, genotype, phenotype? There is no absolute scientific proof.
With respect to my own addiction, it doesn't matter. I am. The treatment? Don't drink. And learn how to be an adult.
There is no doubt that children of addicts are far more likely to have a whole litany of behavioral, developmental and emotional issues...including addiction. Of the five kids in my family, 3 of us are addicts with mental health issues, one is not an addict but has debilitating mental health issues and the last...well, dunno, he seems to have turned 'ok'. Although he's kind of an azzhat.
I watched my parents drink daily, my father to extreme excess. And here I am. An addict.
Important: Kids don't do what parents say because they are too busy doing what they DO. Period. So the best antidote: Recover and don't use drugs and alcohol around your kids. And set an example of how to deal with life on life's terms. Kids watch their parents like hawks. Its how they learn. All the gabbing in the world just goes in one ear and out the other.