There are some controversies where no amount of discussion seems to make any difference to either side. I think this traces to something that our geometry teachers called an "axiom". At the beginning of every logical system, of every rational argument, and of every train of thought, there is some starting point. The first point in any argument is assumed as given. If you don't believe that something is assumed in every argument, then consider this: the first point must be assumed; otherwise it wouldn't be the first point. If that point is not assumed, if it rests on something else -- then whatever it rests on would be the first point -- and that would be assumed. (For those who remember geometry -- which is the first formal system of logical proof that we meet in school -- the "axioms" are the things you assume from the start, considered so fundamental that there is no need for proof. Every other proof rests on those assumptions. More than that: every other thing that we know can be figured out from a good set of axioms. It is just a matter of time, and discovering all the basic axioms, and applying ourselves to reach all the other available knowledge.) So an axiom is something that is is so basic that it is impossible to prove, something that is assumed based on general life knowledge and common sense: like the idea that there is a straight line that connects any two points.
Atheists have a basic axiom about the world: There is no supernatural. It is generally agreed that no reasonable person acts as if things exist which do not exist. So they conclude that anyone discussing the supernatural seriously can't be a reasonable person. By the same chain of logic, any document that records (or claims to record) supernatural events must be unreliable. The other side is not given a fair hearing because the basic belief that there is no supernatural -- the axiom of atheism -- makes it impossible to give a fair hearing to those ideas.
Different groups of Christians have different axioms about the world: That the perfection they attribute to God also holds true for either the Bible, or for the church, or for the pope, or for their own personal moral compass. (I have met a good number of Christians who believe that the Bible is fallible, but that their own personal moral compass is the infallible thing. Of course they're open to instruction -- just not from anyone who disagrees with them on anything important.) So, depending on what their own starting point is, each group will conclude that anyone who believes the Bible contains mistakes (or that their church has a mistaken teaching, or that their personal moral compass is off) is simply wrong. We may hear different explanations as to why the other person is wrong. We may hear some kinder explanations -- but usually the explanation comes down to an accusation that the other side is blinded by the evil one or morally defective, along with complaints about the supposed lack of intelligence shown by those who disagree (by the act of disagreeing). Again, different views are not given a fair hearing precisely because that person holds some belief as an axiom. Any axiom will make it impossible to consider things that might contradict that axiom. (An axiom for the religious person is not exactly the same as dogma, but they are related.)
Everybody has axioms, and it is not wrong to have an axiom. You can't
start any train of thought without one; they're necessary. Where would
any serious thought have gotten without solid ground and a place to
And the fact that two sides won't listen to each other is not, by itself, proof that the beliefs are false. But it is proof that these particular beliefs cut off meaningful conversation with opposing views if they are taken as "given", as axioms -- as things that are not open to discussion. As long as someone holds those beliefs as axioms, they hold the view that the other side cannot possibly be right and that the opposing view is not worthy of discussion. Conversations between the two groups are generally full of personal attacks questioning the other side's sanity, intelligence, humanity, or morality.
The usual way forward is to suspend the axioms -- or take a softer version of them -- for the time it takes to have a discussion or a debate about some other subject of interest to both sides. But generally it doesn't work. The conversations get right back to amazement and disbelief that the other person starts where they start, and assumes what they assume. No matter what else is being discussed, those basic beliefs never quite leave the table, and the other side never quite gets a fair hearing. Each group leaves the conversation even more firmly convinced than when they began: the other side does not give them a fair hearing and never intends to do so; the conversation was not held in good faith but was merely a show for their own supporters; and the other side is completely blind to the things considered self-evident and obvious on the other side of the divide.
It may be more helpful to put the axioms themselves on the table for discussion. If we put the axioms themselves up for debate, what would we ask? How about this: Do you believe that this axiom is the only possible explanation that fits our experience? Or, can we test this idea against another, and see which one makes better sense of a set of facts?