Why do people call themselves Atheist, when they have to acknowledge there is a God not to believe in?

That doesn't make sense.  I know what you are trying to do is attack the logical viability of atheism but you really haven't.  I could say that there is a pink elephant in my bedroom, you could choose not to believe I have a pink elephant in my bedroom.  You choosing to not believe in the elephant doesn't mean you have acknowledged the elephant's existence, it simply means you have considered the possibility of a pink elephant and decide that the idea is just silly.  It's much the same with atheism, one considers the idea of a god and decides that it isn't something that they believe in, one does not need to acknowledge gods existence to not believe in god.

WOW! I know some people who are Atheist and it annoys me. And sometimes we'll argue but never get anywhere. But this question is amazing, It's so simple but true. For an Atheist to not believe in God, they have to first acknowledge that God does in fact exist. *Applaud*  #Legit

I don't believe in Athiests. LOL
But seriously, I think if they honestly and truly didn't believe in God, they wouldn't be so afraid of us Christians making fools of ourselves. I know I feel that way alot. 
So in my professional opinion, they do believe in God. But Satan has gotten ahold of them (by their own doing) and has convinced them that there is no God.
"There are none so blind as those that will not see" So if they don't want to see the truth, then I suppose that is their problem. I do what I can.

Of course, there are many atheists in the world, they have the choice, but I think,in the life we have to believe in, however who is it? As we can live peaceful.Anyway, everyone has the choice, right?

We have to say that so that religious people can understand. Personally, I hate the word for this precise reason. For me, there is no God. There never has been. 'Atheist' means 'without God'. Why should I have to say that there is a God, and I'm choosing not to believe in it? I shouldn't. It isn't fair and it's just a way for religious people to feel good about themselves, as though they have something more than us.