The problem is that you want to insist that atheism is "I don't believe you"...
Which it is.
...when "I don't believe you" is just skeptism.
In this case, specifically about god propositions.
Atheism is "I disagree" (with the assertion that God/gods exist). Which then leaves it to be interpreted only one way (no gods exist).
Of course it doesn't. You don't seem to get how language works. Just because we can call atheism scepticism (I don't believe you) specifically about god-claims, doesn't mean that said position cannot be included in the definition of another word.
And the reason that "I don't believe you" is not atheism is because it also applies to agnosticism...
Which isn't a reason because, as has already been explained to you multiple times, they refer to different things: belief and knowledge. Even if it wasn't the case, natural language doesn't work like that.
Which makes defining atheism that way meaningless and pointless.
Of course it doesn't. It means we don't believe you (because you haven't made a case for your god proposition) but we cannot possibly be 100% certain that it must be false. This is really, very, very simple.
It's not even like god-propositions are in a different category to anything else. Until and unless I'm given good reason to believe
any proposition (including scientific conjectures or hypotheses), I'll have the same stance. Namely, that I'm not going to take it seriously until you give me good reason to.
But you and others here refuse to accept that logic..
Foot-stamping about what things are allowed and not allowed to mean, despite their accepted definitions, is not logic.
...because you can't logically defend your atheism
It's trivially easy to defend. What we can't do is defend a position we don't actually hold.
...and you desperately need some way to avoid having to do so. So you hide behind the insistence that your atheism is just "I don't believe you". When the truth is that you do believe that no gods exist.
It looks far, far more like you're the desperate one in this conversation. I'd be asking myself why I desperately wanted atheism to be illogical, if I were you...