Kicking an addiction, I believe, requires becoming a new person, to some degree. It requires a central totem of hope that one can hold onto, mentally, when one gets into trouble. If your body is calling out for a drink, you have to find the will to resist somewhere. AA groups help because everyone supports you. Unfortunately, you can’t be in an AA group 24 hours a day.
Now some people can create an idea, and hold onto it, and gain the strength they need to succeed. For most people, that is not possible, and they need outside help. They need something outside themselves that is there all the time, or whenever they need it, something they can talk to, who can answer them.
All of this, of course, happens inside their heads. People who kick the habit with religion or not are probably the same in most ways. The difference is how they characterize or envision the voice of encouragement and sanity.
There is a 2000 year tradition with Christianity, and that creates an image with the weight of centuries of belief. It is compelling, and it makes that image or idea become very strong. When that voice talks to you, and you believe it is all powerful, then you have to do what it says, no matter how hard it is.
If you succeed at breaking the addiction, you attribute it to the “voice” you heard that guided you to safety. [Jeruba just put up a post that made this point, too]. It reinforces your belief. Why not stick with it?
Since most quitting models are based on religion, people feel they owe religion. However, it would not be hard to design a quitting group that created an equally powerful image that speaks on behalf of quitting. It just isn’t done very often.