we're dealing with people, here, who constantly proclaim how logical and evidence-based they are.
That strikes me as ridiculously dishonest piece of hyperbole. Whenever I see a sweeping generalisation about a massive demographic, it sets off my sceptic alarm.
I am an atheist, and I have literally never ever said anything like that. I have conversed with many other atheists, and read many more, and I literally can't call to mind an atheist ever using such a ludicrous piece of bombast as that?
I think you're presenting a straw man stereotype you know is untrue, in order to fit with your agenda here. The fact you have littered this thread with obvious misrepresentations about basic word definitions, suggest you're being less than honest.
However it doesn't matter, as what any atheist does or does not claim, a) doesn't change the definition of atheism, which is a lack or absence of belief, and makes no claims or assertions, and b) no theist can demonstrate any objective evidence for any deity when they're asked. Now while that does not disprove the existence of a deity, it is a sufficient epistemological reason to disbelief the claim. If the deity imagined is an unfalsifiable concept I would also remain an agnostic about it, as I must about all unfalsifiable claims, If you don't understand that, then you clearly don't know what agnosticism means, or what an argumentum ad ignorantiam fallacy is.
Who so far seem to be having a great deal of difficulty coming up with either of these in defense of their chosen atheism. One would think that would give them pause for thought
I will assume you mean defence? Though with your track record of illiteracy I may be wrong. However insisting someone disproves a claim is an argumentum ad igorantiam fallacy. That should give you pause for thought, given the irony of your demands that other must be rational.
I don't, nor have I ever claimed a deity does not exist, but I do disbelieved claims a deity or deities exist. I no longer expect a candid response, as it has become quite clear that you have something of a chip on your shoulder about atheism and atheists.
IF they could stop knee-jerk auto-defending themselves long enough to pause for thought.
Try honestly addressing those defences, instead of blindly and dishonestly repeating your own prejudices against atheism and atheists, and of course consult a dictionary.