The definition of agnosticism by RationalResponse is a modern corruption used primarily in psychology to describe god claims as ultimately unknowable. The more accepted meaning, and the one defined originally by Thomas Huxley, is that in the absence of evidence you cannot claim to know.

To say you doubt the existence of god is a knowledge claim because you are stating your position on the spectrum between truth and false.  To cast doubt is to simply place yourself closer to the false position. So the question becomes, what evidence do you have to say god does not exist?

If you lack evidence yet feel this doubt in your bones, then you are indeed an atheist. To an agnostic person, an atheist is irrational, though not to the extent as extreme theists who make extraordinary claims with no evidence. 

The argument of double negation used in paragraph two is illogical because of the assumption that there are only two positions you can take; believing or not believing. So why can we not take a third position, which is “I cannot claim to know either way”. This position is perfectly rational and is simply a statement of having no evidence, or that the evidence in your judgement balances equally; in either case it means that you are a traditional agnostic.

How will you answer this question; did I (author) eat cereal today for breakfast? According to your atheist double negation argument, you can only say Yes, or I doubt it. Clearly both positions are inadequate. 

Further, if you feel in your bones that you are closer to the theist position, but accept you have no evidence, then again you are agnostic. It is the admission of “no evidence” that makes you agnostic. In fact this is the very position that Huxley himself took; Discussing Christian doctrine he says “Give me a scintilla of evidence, and I am ready to jump at them”. 

Furthermore, what if your belief system has nothing to do with god? A spiritualist, a mystic, a belief in the interconnectedness of the universe, Serendipity, Synchronicity. The word atheist is totally inadequate because as you rightly state the root derivation of the word theist is “God” and there is no room for those who reject this supreme entity outright. Agnosticism however is compatible because instead of using the archaic concept of God, it uses a broader terminology; “anything beyond and behind material phenomena” (OED).  

By the way, I am more than happy to change my own terminology as it seems many members here have.