"I do not believe in the existence of atheists"
Belief is an irrelevant concept. Only acknowledgement and acceptance of facts. I exist. As do the good peeps of FSTDT. As do the other 6 million + people in the world. Even you exist (unfortunately). Your so-called 'God' doesn't. Next question.
"No, this is not a play on words or a trick statement"
...but it is.
"Atheists don’t exist"
I exist. As do the millions like me. Deal with it.
"By “atheist” I am referring to the ideal person who does not believe in the existence of God, not the person who labels themselves as an atheist"
So basically, six of one, half-a-dozen of the other. Be seeing you. [/The Prisoner]
"Clear as mud?"
You said it. I didn't, pal.
All people who label themselves as “atheist” are not, by definition, atheists, because they all believe in the existence of God"
Are you a follower of Allah? No? Well you are. As any Professor of Theology (and thus, by definition, know infinitely more about your beliefs than you do) will tell you, 'Elohim' (as Jews refer to him), Allah, and your Judeo-Christian 'God' are all one and the same.
Do you beleve in the existence of - and worship - Rama/Vishnu (or all his myriad forms)? The Earth Goddess? L. Ron Hubbard? The Invisible Pink Unicorn? JR 'Bob' Dobbs? The Flying Spaghetti Monster? Haruhi Suzumiya? No? Well then, that therefore makes you an Atheist. After all...:
We Atheists merely believe in one less God than you.