So by your logic, when I say that the Easter Bunny doesn't really exist, I am actually confirm that the Easter Bunny does exist. On a trivial level this is true - by using a term to refer to the idea of God or the Easter Bunny I am necessarily acknowledging that they have a certain linguistic existence as ideas which can be roughly put in to language. But that doesn't "confirm" they have an independent physical existence, and beyond that trivial point what you are saying doesn't make any sense.
I'm not atheist, but your not right with this question.
these A-theists dont believe as if to say they are shutting their eye's real hard and saying the sun doesnt exist anymore.
they truely believe they know with facts in their head and lack of proof in their own lives that a Creator or any god exist.
try to do some studying on the idea of being an Atheist for a change.
I'm a christian and even I know that these people although somewhat delusional in my point of view, have their Proofs and are not imagining and manifesting a lie from having seen the truth.
they are not Arrogant by choice. they are simply people who are set in their ways and dont want to believe what is not in their lives.