Capgras Delusion - believing all your friends and relatives have been replaced by aliens.
Doctors think its because a small stroke in the brain has disconnected the part of the brain where they recognize faces, and the part that gives them their emotional responses. They don't feel anything when they see someone familiar, so the only explanation is that they are no longer the person, even though they look the same. And of course, if you tell your wife that, she tends to get quite upset, thus proving your belief is correct.
Same with Cotard Delusion - patient no longer has any emotional response to anything, so must be dead. When a doctor is confronted with this (rare) delusion, tries to prove the guy wrong. "Do dead people bleed?" "No, of course they don't". (Stab with needle, drawing blood). "Well, I'll be damned, dead people do bleed."
They are well aware that the evidence makes their belief seem incredible, but they will politely inform you that in their case it just happens to be true.
Point is that people are utterly convinced that their interpretation of the situation is correct. They are not swayed by outside evidence or rational argument. What they think trumps any evidence.
Shouldn't need to hammer the point, but it illustrates how our brain works - we totally ignore scientific facts if they contradict our internal beliefs.