There is no subject on which the illusion of asymmetric insight could be more relevant than the ways in which religious and non-religious people presume insights into each others minds. The religious person, and most famously in the West the Calvinist presuppositionalist apologist of the Van Til/Bahnsen variety, works on the assumption that the following two statements declare the truth about atheists.
1) there are no atheists because anyone who is an atheist is deluded about the reality of God
2) Any other atheists are only atheists because they constantly lie to themselves and others about reality.
Then there's the atheists who return the favor given them by presuppositionalist Christian apologists
1) any theists are simply deluded about what reality is by believing there is any kind of god
2) any theists who aren't covered in category 1 are just knowingly lying and suppressing the truth about the reality that no gods exist.
Both groups profess a knowledge and insight into the other that not only supercedes the insight the other group may bring to the table about them, but both groups also profess a knowledge and insight into the other which, by their own reckoning, the assessed group isn't capable of making about itself. This, I suggest, could be seen as how the social cognitive bias of the illusion of asymmetric insight continuously plays out between theists and atheists.
Both groups will steadfastly deny that they themselves are capable of exercising this social cognitive bias. Why? Well, obviously because if I'm right then I can't possibly be bringing a social cognitive bias to the discussion, can I? If my metaphysical position and methodology are right then it's simply impossible for me to display a social cognitive bias in how I denounce some other group. Would it not seem that the definition of a cognitive bias in social assessment is defined by having trouble to observe it in myself when I can so readily observe it in others. As a certain website might put it, you think that you are more generous to others than they are to you, and you think that you don't make categorically positive or negative judgments about others, and you may think you aren't employing a cognitive bias in assessing an entire people group ... but you are not so smart. HT, of course, to You Are Not So Smart.
Of course the sticky wicket here is that simply because you are absolutely sure that your metaphysical position is right does not mean you can't/don't/won't/aren't operating with a social cognitive bias in assessing other people. Having seen how theists and atheists go back and forth it has struck me in the last twenty years that both sides employ arguments within the illusion of asymmetric insight with gusto.
At a sort of subliminal but visible market level this is why theists and atheists have such cottage industries invested in promoting and selling the wares of converts and apostates. See, they exclaim, that this person switched sides is proof that even if you grew up thinking A then you can discover B is the truth over against the upbringing you got with family and peer pressure. Well, all right, but this sort of marketing gimmick employed by both sides is a kind of concession to an awareness that asymmetric insight is a risk. This is why atheists like to pitch books by ex-preachers particularly, just as Christians like to pitch the conversion of an atheist into a theist, even if that atheist "converts" to some deistic form of theism that has nothing to do with the faith claims the theist is really interested in defending.
I admit here I have what some would call a low anthropology. I have not observed that the greatest and highest virtue of humanity is its intellect or capacity to reason. Sure, technically humans can and do reason but even the most ardent materialistic naturalist committed to both methodological and philosophical naturalism would be hard-pressed to say that in the last 24 pack of millenia that human progress has suggested we are getting that much "better". So the Enlightenment happened. At length the Enlightenment led to the Industrial Age and the Industrial led to the Age of Imperialism and then into the 20th century.
We have greater advances is science and technology now than ever before and now we have so many people that people fret about the inability of the biosphere to sustain all the human life our amazing technology has permitted to live. There's a whole field of medical practice of which I am a grateful beneficiary that has not existed as a viable medical practice for even about fifty years, so far as I know. We developed nuclear weapons that hippies and doves feared would obliterate all life on the planet for five decades, a dread that the Cold War could only end in a Hot Death for the planet unless everyone united for multilateral disarmament. And yet here the planet is.
For all the shrieking and screeching about how insane and made and terrible other people are, you know, the people who don't think exactly the same way we do, it appears the planet is still around and humans are still breeding (even though, apparently, they shouldn't but it would appear the laws of nature has not-quite-designed humans to be eager beavers in the breeding department and sex, so I'm told, is apparently enough fun for people to overcome all sorts of trial and error of "doing it right". But if the planet has too many people why don't people just, you know, resist the urge to get laid? Oh ... perhaps that would be because much of the world is rather broadly straight and desire cannot be denied or something like that? I have sometimes wondered why secularist overpopulation types don't advocate celibacy more. It would seem to make sense ... .
But at any rate, what does it matter if free thinkers can tell Christians the Church is anti-sex while the Church has so many voices speaking against birth control because sex naturally tends to lead to babies. Well, we can't have that and people should have sex because it's a natural drive ... but there are too many babies being born and there should be fewer of them ... but if there is a danger of overpopulation then the whole desire to have sex in itself must be both irrational and destructive to the biosphere and we should instead consider curtailing the sex drive to prevent overpopulation rather than constantly attempt to employ sex in a recreational fashion. When I have stepped back further and further to try to get a sense of what might be reasonable or unreasonable on either side I began to realize that reason wasn't really looking like a whole lot of what was important to any human position. Humanity is capable of remarkable but selective reason. We're geniuses at making cases for what we want or feel we need but it would seem that our strengthes have corresponding weaknesses.
Consider a recent idea in brain research and psychology, the proposal that belief in a god can be construed as an extension of what is known as "theory of mind". "Theory of mind" is essentially our capacity, as humans, to imagine what it is like to think and feel as someone else does. If someone is otherwise completely functional but unable to conceive of what it is like for another person to think and feel differently than the individual does that is called Asperger's syndrome. it's consider on the low end of autism spectrum disorders. A failure to grasp how another person thinks and feels leads to all sorts of social disorder.
On the other hand, if a person has a highly developed capacity to imagine the thoughts and feelings of others but has a sensory deintegration this person hears voices that do not correspond to a sentient being outside the individual's head. Auditory hallucinations and the like indicate, colloquially, that the person be crazy. These used to be the sorts of people who were having conversations with no one you could see back before cellular phones were invented. When I was a kid it was a foregone conclusion that any person walking around seeming to talk to nobody was nuts. Now, well, they could just be using a wireless headset so you aren't quite sure. Either way that person still seems to be not entirely aware of what's going on around them.
But, say some philosophers and scientist, the tricky part about our capacity to imagine the thoughts and feelings of others is that we are capable of imagining the thoughts and feelings of someone who doesn't exist. Ergo, God exists in our minds because we have conflated our capacity to imagine and empathize with real people into a belief that sentient beings we can't observe also exist.
But this is not all, we can also anthropomorphise creatures that don't really display any comparable intellect or capacity for linguistic communication. Take the Pixar film WALL-E. Take any of the Apes movies. There's no way an army of non-human primates is going to conquer the human race with it's six billion population, firearms, nuclear weapons, biological weapons and collosal capacity for conceptual and linguistic communication. The only beings that can imagine that such a primate conquest of humanity are folks who go by names like Gorilla Grodd ... or Mojo Jojo. I think I'd rather have dinner with Mojo Jojo all things considered. He seems to have better taste in music.
Now I know atheists and theists alike may think I'm completely wrong in putting things this way. That's part of what prompted me to write this. It seems as though the theist and the atheist habitually work from the illusion of asymmetric insight while imputing the cognitive bias entirely to the other team. It also appears that so long as you are convinced that your metaphysical position is most likely the really true one you get a pass on even being capable of cognitive biases.
But if the recent theory that humanity evolved the capacity to reason NOT to discover the truth but primarily to win arguments in social settings gains any traction (and it might not, I don't know) ... then both the theologian and the free-thinker/philosopher might turn out to have been guilty of the same cognitive bias without realizing they had something in common. They may turn out to have labored for millenia to prove that reason and logic prove them right categorically when reason and logic don't prove anything so much by themselves.
And despite various appeals to the Laws of Nature the temptation to rework the Laws of Nature where we don't like them seems to be an impulse that crosses a theistic/atheistic divide. Christians want to make gays no longer gay, Dawkins has at points suggested that maybe eugenics is okay to bring back on the table after all, apparently. There are those who think that genetically modified crops are playing god yet if humanity has advanced to the point where we can more directly manipulate genetic outcomes than our history of breeding specific kinds of dogs then it seems that "reason" is always put in the service of other things. Humans seem to be brilliant at rationalizing a lot of decisions that are not as rational as we keep telling ourselves they are.