"I understand that SOME atheists want “atheism” to mean the absence of a belief in a deity"

Well that may or may not be true, but it's entirely moot as that *IS the dictionary definition, which is (like all words) derived from common usage. So whether anyone accepts it is a moot point. I define my position as lacking the belief that any deity or deities are real, so by the dictionary definition I am an atheist. The label is not important nd only a useful word to clarify my position is a lack of belief in a diety. If it were defined differently then it might not apply to me, and I get the impression from a lot of these discussion with theists and religious apologetics that they *WANT to redefine it so they can reverse the burden of proof, Breezy does this all the time.

"SOME dictionaries define it that way."

All dictionaries define it that way, though they may have secondary definitions that are less commonly used. Again this is true of all words.

"But that essentially is the result of a mistake about the etymology of the word."

I don't think this is true but even if it were what difference would it make since the word's primary definition exactly defines my position? So when I say I am an atheist everyone can know instantly what I mean, and not what many theists who don't like the definition want it to mean which is irrelevant to my position?

"I certainly do not accept that definition (which is only one among many)…so that may explain why I say what I do. (We can discuss its etymology if you want.)"

Well I'd rather discuss why you don't accept the dictionaries primary definition, if you feel it doesn't apply to you then you can clarify your position, rather than try and change a word definition that is how most people define it already. I also hear this a lot, usually from American theists who try to redefine the word for their benefit, to avoid the burden of proof for the claim a deity exists.

"whether or not any gods exist)…the words “believe” and “belief” are merely disguises for a blind guess."

I don't agree, and the rejection of a claim doesn't carry the burden of proof, it is according to philosophical epistemology the person who makes the primary claim that has the burden of proof in any discussion.

"There is no way to KNOW that gods exist or not. Both are possible."

Two errors here sorry, firstly your initial claim would need to accurately define a deity before we can know what evidence there is for them or to refute the claim. Your second claim seems to contradict your first, if there is no way to know whether a claim is true or not, then you can't say whether either position is possible. What objective evidence can you demonstrate to show a deity is possible?

"Theists claim it is more likely that at least one god exists"

Oh dear, could you demonstrate objective evidence for this please?

"and claim that the preponderance of evidence points in that direction. "

Really? What evidence is this, and could you demonstrate it please, can any of it be objectively validated, because theists call everything evidence, and I've seen only anecdotal claims and irrational fallacious arguments. I even started a thread on here for someone to demonstrate any objective evidence for a deity or deities and no one could offer anything but the fallacious arguments and anecdotal claims I mentioned.

"Atheists claim it is more likely that no gods exist…and claim that the preponderance of evidence points in that direction."

In my experience most atheists don't claim this, rather they point out as I have that there is no objective evidence for the claim a deity exists, and they may offer rational or evidenced arguments against certain claims from apologetics. It is an unequivocal fact that humans create and have created fictional deities, no one can reasonably deny that fact.

"They are using THE SAME “evidence.”"

Nope, what evidence are you referring to for the existence of any deity? Can any objective evidence be demonstrated for the belief? If not then I need no counter evidence, and Hitchens's epistemological razor applies, "that which can be asserted without evidence can be dismissed without evidence".

"Frankly, none of the “evidence” points in either direction as far as I can see. Atheists mostly blindly guess there are no gods "

So you admit in the sentnece that there is no evidence that a deity exists, then describe people who refuse to believe they exist as guessing? Do you believe mermaids exist, and if not is it just a "blind guess" that they don't?

" theists mostly blindly guess there is at least one (the one they worship)."

So an inherently biased position for a start. Atheists apply a consistent standard for belief in deities, and monotheists demonstrably favour just one.

"As I see it, one cannot come to the conclusion “There is at least one god” or “There are no gods”…using logic, reason, science, or math. All one can do is to make a guess in either direction."

Why would you believe something is real when no one can demonstrate any objective evidence to support the claim, and what's more logic and reason absolutely support withholding belief in things we can find no evidence for, this is all before we tackle the claims religions make that are absolutely falsifiable, and many of which have been shown by scientific evidence to be false. Creationism is a superstitious belief with no evidence, evolution is a scientific fact that has 150+ years of scientific scrutiny to support it, and remains a scientific fact explained by the scientific theory of evolution. It is a scientific fact evidenced beyond any reasonable doubt that we evolved slowly overtime like all life, and were not created in our current form. To show just one claim by religious apologetics that has been thoroughly refuted by science. Theists of course are understandably in a quandary here and refuse either to accept the fact at all, or try to cherry pick what it means in such a way that they can preserve the belief they have no objective evidence for anyway.

However I am now digressing, the fact is believing in a deity or deities carries a burden of proof by any epistemological standard, and religious apologetics would hardly be the massive industry it is if this were not the case. Whilst atheists are free to make claims and show evidence that supports their atheism, atheism does not require this, as it is simply the absence of a belief which no one can demonstrate any objective evidence for.