At least two prior posters (I've skipped ahead, and may have missed other instances) referred to atheists "not believing".

Let's get the terms straight: "Not believing" is not the same as "believing not".   An atheist, as I understand the term (and sometimes apply it to myself) "believes not". That is, (s)he affirmatively believes, and perhaps argues, that there is no god. Not just Yahweh, but Ahriman, Jupiter, and all the rest of the putative gods.

To "not believe" in the existence of a god is a much looser, less doctrinaire position: "The existence of a god is not clear to me, seems unlikely, and since I feel a need to ride one horse or the other I'll go with the position that seems more likely, to one degree or another." In essence, "I have not come to a position of adopting a position of affirmative belief."

An agnostic is by definition a "can't know-er", and so may be a "can't decider", or tentatively a "non-believer", or go whole hog and be a "believer not". An agnostic may be anywhere on the spectrum from a devout, practicing religionist to a turner-away from religion and religious practice, but can't rationally be a "missionary atheist".

Most of the time I describe myself as an "agnostic believer not", but occasionally, in some moods, I say, "Oh, to hell with academic caution, I'm an atheist!"--(a straight-out, express believer not). But before long I calm down and back away from that doctrinaire position and call myself an agnostic again. Most of the time.

Go thou, with my blessing, and believe/do what seemeth good to you.

Dave Oesterreich