Well, we've had health insurance for my entire life so I guess we had "access" to it, but as far as I know my dad never used it, and I didn't see a psychiatrist until I was 26 (and I wasn't drinking much before that, certainly not enough to be considered an alcoholic). He certainly didn't have access to it until he finished school, growing up in a relatively poor family.
I think at least in my dad's case, he saw how much his dad's alcoholism screwed things up, and decided that he was going to try and avoid that fate no matter what, sort of using his dad as an example of "what not to do." As I was growing up, I think I saw my dad drink a grand total of four glasses of wine, all of which were done on different New Years events, and never enough to get "drunk" or anything like that. As he's gotten older (and as his kids have all grown up), he's relaxed on that a bit and I will occasionally see him drink slightly more frequently, but I think that habit of sobriety has been somewhat ingrained into him at this point.
> Alcoholism seems to run in the males in my family (with the exception of my dad and me, strangely), so this sadly wasn't even really something completely unexpected.
Indeed, familial alcoholism is suspected to be a complex genetic trait (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4056340/). As for why you and your father seem to have been spared by that... if I may ask, did you two have access to mental health care and use it? A common theory in addiction research is the "self-medication hypothesis" (https://www.psychiatrictimes.com/view/dune-and-the-second-co...) - basically, that people accidentally discover during experimenting with drugs that the drugs help with mental or physical health issues.