I would also think that if you expect someone in denial, to admit they are in denial, that can be a tall order.
I think one thing the average non-believer may be taking for granted is the "double down" effect.
A believer often banks on certain things being true, despite evidence to the contrary. Evidence to the contrary may often be seen as a "test" for that matter. When faced with such evidence of a test, a believer may think it more virtuous to "double down" and stick with their belief, as opposed to changing it. The more they can grip it, the more they prove their worth with their belief. Their belief can then stand the test, etc and so forth. To back down is to allow doubt to enter, and thus risk failing the test.
If you begin to doubt and lack belief, I believe this is often seen as the beginning of a slope that leads straight to deception, believing in lies, lacking belief, and thus they may fall afoul of sin, or displease God, or risk their status with God (if they believe that's possible), etc. So for some, to even seriously question certain things is weakness. To double down and hold onto them despite everything to the contrary saying otherwise, is strength and virtue.