The agnostic-atheist — a term basically meaning agnostic (no reason to believe in God), likely used because more people have heard of atheism than agnosticism. We generally ask if people are really atheist or agnostic — if they’re truly atheist and claim no god exists, they accept it on faith, not logic or proof so we don’t have much to discuss as their position stems from faith; no amount of reason, logic, or critical thinking can shake their dedication to their dogma.
But if a person is agnostic (even if they mistakenly call it atheism) we’ve got something to discuss — they believe god doesn’t exist, not as an absolute decree by fiat, but because they don’t see evidence or any reason to believe. We certainly disagree with their conclusions, but at least they’re using rational logic, something the true atheist lacks in their dogmatic claim of “there is no God”.
In short, atheism is illogical and nonsense, at least if you’re agnostic you’ve got some reasoned logic behind your statement — logic and critical thinking the atheist lacks.