There's a problem there. Just because I believe in Y, not X, doesn't mean that my belief should be defined as being a believer in not-X, except according to X believers who are putting themselves into a position of importance which they don't necessarily deserve. By doing so, you give X respect that it's not due in my eyes, because X isn't even on my radar, and doesn't even warrant consideration based on the evidence I'm choosing to pay attention to.
If your definition stands, I'm not atheist (1. Disbelief in or denial of the existence of God or gods. 2. The doctrine that there is no God or gods.), nor am I agnostic (1. One who believes that it is impossible to know whether there is a God. 2. One who is skeptical about the existence of God but does not profess true atheism. 2. One who is doubtful or noncommittal about something.) because my opinion on god is a non sequitur to my belief system, and it's neither a reaction nor any more doubtful than anyone else's beliefs. The question which defines these terms doesn't apply, and is not put....except by theists!