1. You have NOT SHOWN that "atheism" was originally intended to specify only those who claim there is no God. Nowhere have you provided a source that supports this claim. At best you have gone back to the root word ("atheos" - greek) meaning "godless" - and here you merely twist the definition of godless, or cherry-pick one to suit your purpose rather than accept the ACTUAL MEANING of the word.
You thus appear to be deliberately dishonest in your endeavours.
2. Those who claim to not know are "without" until they decide to be "with".
If you don't know whether you want to be indoors our outdoors... where are you? Are you trapped in some temporary limbo of no-space?
Likewise, if you do not know if God exists or not, you are without-God until you choose to be with God.
Having a belief is a binary proposition - either you have that belief or you do not have that belief... and note that not having that belief is NOT the same as believing the opposite.
If a ball is hidden from you, you either believe it is white, or you don't. If you don't believe it is white, do you therefore believe it to be black? No. You just don't have the belief that it is white.
You fail to grasp this simple point.
Not all of them do fall under atheism.
Some agnostics are also theists - believing in God through Pascal's wager (the benefits of believing and being wrong outweigh the risk of not-believing etc).
Atheism is just a question of not being a theist.
If you are not a theist... you are an atheist.
1. I have not cherry picked anything to make "atheism" suit what I feel is best. Take it or leave it, the term was originally intended to describe those who reject "theism" in the sense of the claim "God exists" is false.
2. Those who claim to not know are not without until they decide to be with. This is absurd and completely illogical. That is like saying those who claim to not know are with god until they decide to be without.
Whether you are indoors or outdoors has no relevance to the state of where you want to be. You wither want to be in, want to be out, or don't know. You could be inside or outside. Somebody who does not know will not claim to want to be indoors as much as he will not claim to want to be outdoors.
Having the belief is a binary position. You either have it or do not have it. Those who do not have the belief there is no God are not atheism. Those who do not have either belief do not fall under either ism.
Yes you believe a ball is either white or not white. That is logical. You either believe "there is no God" or you do not believe "there is no God". Those who do not believe "there is no God" either fall under theism or fall under an ism.
Those who do not claim there is no God cannot be said to be Godless. One who does not know, neither abides by the claim that God exists or God does not exist.
Claiming that atheism is "all who do not abide by the belief that there is God" is no different from claiming theim is "all those who do not abide by the belief there is no God".
Theism and Atheism are positions in a matter. One who does not know whether or not there is a God is not claiming there is or isn't one. One who is not claiming there isn't a God is not "without God" as much as he is not "with God". In order to be considered "without God", one must take the position being "without God".
In actuality, Godlessness or without God is simply that the universe, not any particular person is without God. Thus, the position a person takes is irrelevant to the actuality of the person being Godless. If there is no God, then all theists are Godless/Without God. If there is a God, all are not Godless, but with God.
One position claims that the universe is with God. The other position claims that the universe is without God/Godless. Those who do not know certainly do not make the claim that the universe is with God. Those who do not know certainly do not make the claim that the universe is without God. In actuality, one can either be with God or without God regardless of what claim they make. You either claim that all are Godless or none are Godless.