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In order for one to "withhold" belief in dragons on Mars one must affirmatively believe that it is possible that they don't exist.

What a bizarre statement. You seem so desperate to prove that atheism involves "belief" that you're inventing new logical rules for assumptions, insisting that withholding belief requires "belief in the possibility of naught". Of course, to believe such, you must also believe that it is possible that it is possible that they don't exist, and you can go several levels deep before you realise that you're wasting your time on semantics rather than logical reasoning. There's also the fact that lack of belief in something can simply be a matter of never hearing of the thing in the first place -- as such, someone who has never heard of god-concepts before and lacks belief as a result is still an atheist.

The idea of nested possibilities when referring to the same possibility is illogical. If it is asserted that something is "possible to be possible" then the only alternative is "impossible to be possible" which exactly the same as simply "impossible". No matter how many layers deep you go the meaning remains the same---the root possibility is either possible or impossible. I don't understand how this can escape you.

As for those that never heard of god-concepts----I have a hard time seeing how this is relevant. The child who has never been introduced to the concept of an airplane, and that people can fly through the air in one, obviously doesn't have an opinion on it. He has no belief or non-belief. There is no concept, in his mind, from which he may withhold his belief. As soon as someone introduces him to the idea (but does not show him an actual airplane) he has three choices----to believe it is true, false, or withhold the decision until more information becomes available. Upon introduction to the idea, contemplation about which of the three choices to make is inevitable. You have heard of the idea of God or god(s) so you can't claim ignorance about the subject.

Besides, even if we define a-theism (or a-aeronauticalism) as not having belief or disbelief in a concept one knows nothing about, it would not apply to you. If one is truly an a-theist in this sense one does not even know that one is an a-theist and as soon as one is informed of this one ceases to be a-theist. Therefore by your own definition you are not an a-theist. You are a disbeliever. You affirmatively believe God or god(s) does not exist.

At any rate your insistence on disingenuously arguing even with the vastly agreed upon classifications of atheist, agnostic, and believer is indicative of either psychological problems or just antagonism towards those on the other side of the debate. Trying to smite God by saying you don't even acknowledge the decision you have made in your own mind just makes you look ridiculous.