Also note that it's not only theological propositions that are impossible to prove: The omphalos hypothesis could be true and the whole universe could have started existing a microsecond ago. I could be a brain dreaming in a vat, or a simulation, and no one can prove that isn't the case. Should I be 'agnostic' about that, too?
For example, agnostics are not theists, therefore they are a-theists - according to one possible definition of the term. Similarly, ignostics do not take a position on the existence of gods, therefore they are agnostics - according to one possible defintion of the term. In both case, you could argue that agnostics are not atheists, or that ignostics are different from agnostics. That does not mean that the binary classification theists/atheists or the tripartite classification theists/agnostic/atheist is wrong - it just means that you're asking a more nuanced question that requires a more nuanced terminology.
In any case, we're drifting way off-topic here. It's fine if you don't agree with what I think atheism is, although I would be interested to see what kind of definition you base it on. Aside from the definition (this means an outside source, not just something you write down here) I'd also be curious what you see as the difference between agnosticism and atheism.
All ontological claims are unprovable, resting on axioms that have to be accepted on faith. I can't prove I just wrote you this message, I just believe I did. Philosophically speaking, there is no certainty.
I would be interested to see what kind of definition you base it on
Binary classifications are useful. There are people who affirm the existence of gods. Let's call them 'theists'. There are people who are not members of that group. Let's call them 'a-theists'. Done.
Now, you might be interested why people do not affirm the existence of gods. For example, they might think it unlikely due to empirical evidence that contradicts most traditional religious claims. Or they might think there's not enough evidence to come to a conclusion either way. Let's call the latter agnostics and make our binary classification into a tripartite one. But wait, what about ignostics, believing that the question itself is ill-posed? Should we include them as well as their own category? What about all the other ways not to be a theist? You have to draw the line somewhere if you want to avoid an explosion in complexity.
None of the possible ways to draw the lines is inherently more correct as long as you take care to define your terminology, it's just that you might upset different groups of people because they feel underrepresented or resent being grouped together with 'those guys'.
God can exist, I could be Superman.
> God can exist, I could be Superman.
That doesn't sound like a rational argument to me.