Saying it does not make it logically coherent.
True enough. Try me.
Would you agree that atheism as you are referring to it is defined by a lack of belief in god or believing no god exists?
Yes.
Would you agree that these are two separate things?
Sometimes. Not always. You seem to be assuming a substance and stability to god-beliefs that I do not think can realistically be found there.
"Deities" are up there, very close to the ultimate freestyle concepts.
Further would you agree that a lack of belief can come from an inability to believe that a god exists or that no god exists?
A technical possibility, I suppose. We would have to establish how to detect a deity before a meaningful answer could be given.
This inability can come from either a lack of knowledge regarding the concept or a lack of ability to believe.
Among several other possibilities, sure.
If so there are now three differentiating circumstances that vary distinctly all for which you would use the same term when it could be easily circumvented. Sounds like you want equivocation.
No, I just don't want to encourage the perception that deities, gods and theism have inherent substance and delimitation.
All of those are human creations, and particularly ill-defined at that. We all should acknowledge that and mislead ourselves no more.
Those who want equivocation, consciously or otherwise, are those who treat those three words as solid ground for establishing other ideas.
It is much more pragmatic to make the first distinction a belief and the lack of a belief as two separate categories.
Is it? Why?
Especially when one of the categories revolves around a lack of knowledge which is related to agnosticism. And the last, well if there is an inability to believe then it isn't really applicable to them anyway.
Unfortunately, all of that effort of yours crumbles to the ground from the get-go, because the core ideas are much more malleable and capricious than they would have to be for your definitions to have true meaning.