It is hard to imagine how one can have any evidence in support of a belief they do not have.
Agreed, just as it's hard to imagine how one can have a belief if they do not have supporting evidence. The proper correlation is, sufficient evidence leads to belief, insufficient evidence leads to the withholding of belief. The other two logical possibilities don't work - not believing in the face of sufficient evidence, and believing without it.
if one defines atheism in this manner (as a lack of a belief), then it follows that there exists no beliefs that atheists have which can distinguish them from theists.
Correct. The atheist is identified by one particular lack of belief, If you want to know if somebody is an atheist, ask him if he believes a god or gods exists. When he says "No," there's the lack of belief that is the sine qua non of atheism.
I guess we just get tired of being lied to over and over and over again by people who are being completely illogical yet proclaiming themselves to be the epitome of logic.
I feel your pain.
So your goal is to teach critical thinking to those who solely rely upon beliefs.
No, I'm not trying to teach critical thinking. I try to use it and only it when deciding what is true about the world, but it is learned not in Internet discussions, but through years of high level academic pursuit. You learn it in your first evolution class, when your professor lays out the evidence Darwin had and gives his conclusions and the reasoning leading to them. That's how it's learned.
And I rely solely on beliefs, as does everybody else. Some of those beliefs are held so strongly that I call them facts. To my knowledge, none are based in faith.
having religion is the best way for all the kiddies of this world to learn and grow. How many problems would never come out without religion? If the problems do not come out, they are very hard to solve.
I disagree with the first sentence. What kind of problems come out with religion, and how does religion help solve them? I just listed some problems caused by it:
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In the case of Christianity, it's pretty clear that they neither understand nor respect human beings, and create a ton of problems because of it. They tell people to not be gay. Not helpful. Generates self-loathing and homophobia. They tell priests to be celibate. That was a disaster. They recommend abstinence only. What'll we name the baby? They try to criminalize abortion, and where successful, unwanted baby's are born to those that don't hemorrhage to death in an alley or filthy clinic first. They describe humanity as weak and dependent on a god. They do violence to reason by praising faith as a higher virtue. Not helpful. It's practice for later in life when they believe other things by faith, such as that climate change is a hoax, or the vaccine is more dangerous than the virus, or that an American presidential election was stolen. That kind of thinking is the legacy of Sunday school."
What benefit can you show to offset all of that, and I mean a benefit that we need religion for? Universities, hospitals and food kitchens don't require religions. What does religion give us that we get nowhere else that is of sufficient value to offset all of that harm I described? Nowhere, which is why its disappearance is a net positive.
That's my argument. Here's a pile of harm from Christianity, the dominant religion in the West, and insufficient good to offset it. You can rebut it by showing me the good religion and only religion can provide, and explain why the negatives I described above aren't really negatives or are more than worth absorbing if you believe that. You can talk a critical thinker out of his antitheism if you can demonstrate that it is unjustified.