Hi Olinda and welcome! I'm no expert but from my experience with my AH I think that even though they may admit it, they don't truly believe it deep down inside and just say it because we want to hear it. My AH admitted he had a problem and tried quitting many times. He quit for a week or so many times, and I think that was enough to convince himself that he didn't have a problem and he would go right back. The last time he tried to quit on his own he ended up in the hospital, on a ventilator for 10 days and almost died, and then the lightbulb went on and he finally realized he was an alcoholic. He started going to AA daily and has now been sober for close to 60 days (although I suspect he may have been drinking a bit recently, but that's a subject for another thread). Admitting you have a problem is just part of it, they have to acknowledge it, accept it and truly want to change it.
Others much more knowledgeable will be along shortly. There is such a wealth of information and support here. In the meantime, keep posting and read the stickies at the top.
Good luck!