The idea is that even if atheists don't believe in God, they must believe in some sort of higher power. Maybe they believe in Science, Reason, Humanity, or The Universe, they must believe in something!
- We admitted we were powerless over alcohol—that our lives had become unmanageable.
- Came to believe that a Power greater than ourselves could restore us to sanity.
- Made a decision to turn our will and our lives over to the care of God as we understood Him.
- Made a searching and fearless moral inventory of ourselves.
- Admitted to God, to ourselves, and to another human being the exact nature of our wrongs.
It just doesn't work that way, not for everyone. Some non-religious people would be okay with that, but many others would not. I suppose it could be said that I believe in the value of science, reason, and the universe, but I certainly do not have the same attitude towards these that religious people have towards God. Science and reason, as important as they are, are just ideas. I just don't think of them as "higher powers", in much the same way I don't consider literature, cooking, or the great outdoors to be higher powers.
More concretely, they aren't things I pray or meditate to. Maybe some atheists do that, but I bet most don't. It also doesn't make much sense to ask these "powers" to remove defects of character, or to confess our wrongs to them. I don't think I could turn over my will to them. I might agree that critical thinking helps me become a better person, but only in limited situations and through a completely different process.
And this is not just a matter of poor translation. I feel that even the most charitable atheist, who is trying to interpret the words as they are intended, might still have problems with it. Sometimes there is no translation. Just like there is no one-to-one correspondence of words between languages, there are some concepts in religion that just can't be translated to a secular worldview. "Higher power" is one of those. "Faith" is another. "Sacred" is another.
Or maybe there's a translation, but it's strained and uncomfortable. I can see some atheists being comfortable with "higher power" language, but I wouldn't bet a reputation for inclusiveness on it.
While we're at it, this is also true between different religious traditions. There's not always a good translation of concepts. Even things like "faith" or "god" are only approximate translations between religions.
That said, I have nothing against Alcoholics Anonymous. I think it is entirely possible that it is inclusive of non-religious people. If this is the case, then I merely argue that this is not by virtue of their "inclusive" language.