state: noun: The particular condition that someone or something is in at a specific time.

NOT possessing a belief is a STATE of existence. It is not a principle, or a belief in itself, or a cause. And that's not true just "because I say so", it is rather easily demonstrated.

Do you currently hold the belief that there is a rainbow colored unicorn orbiting Jupiter riding in a teacup? Is that something you currently believe to be the case? Yes or no?

If X =A then not X also = A

Hmmm, interesting logic. and by "interesting" I mean entertainingly ridiculous.

Also, atheism isn't "anti-theism". Nor is it a cause, a principle, or a system of beliefs. It is a state.

"Atheism is a person who states that there is no god. Therefore they do not belief because none exists. This is a statement said as a fact. "

Well gosh, thank you so much for telling me what I say. I had no idea I said that before but now that you've stated it well... it just must be true!

I wonder why I don't remember saying these things. Perhaps I have amnesia?

Or... and bear with me here because this is a wild idea...

...you have no understanding of what atheism is.

Someone lacks an understanding of atheism here... but somehow I doubt it's the atheists themselves.

The statement you quoted is correct. Atheism is the LACK OF belief in the existence of a deity. That category includes, but is not limited to, people who state flat out that such deities do not exist (sometimes referred to as "strong atheism".)

That you seem to think a proper explanation of the meaning of atheism represents a misunderstanding of atheism would indicate you yourself are ignorant of what atheism is.