The problem comes in when people take a positive stance against ever trusting the use of reason. Where they see someone stepping back, and dealing with a topic dispassionately, and alarm bells start going off. They immediately distrust the person, and if their conclusions contradict the gut intuitive reaction they have to a topic, they will side with the intuitive reaction. The 'intuitive reaction' of human brains is essentially documented in any comprehensive list of common logical fallacies. They were things we feel ought to be true, but we know are not. Things like a terrible person can't make good points, if a person is wrong about one thing they must be wrong about others, if things happened close together spatially or temporally they must be causally connected, if something is natural it must be better than artificial, etc. At that point, it doesn't matter if anyone in the group is practicing metacognition and solid reasoning, because they will be actively resisted for precisely that.
Societies view of intellectualism changes on the scale of centuries. It was at a height before World War I, almost to the point of fanaticism. It made people willing to believe that science and reason would usher in a utopia by default, because it was not capable of doing otherwise. Then, mustard gas rolled down hillsides into trenches. Mechanized tanks crawled battlefields. The creations of science were used to wreak the most horrible suffering, and society paused at that. By the time the concentration camps were unveiled after the end of the eugenics (all widely accepted as true and reasonable by the scientific community of the time), the horror wasn't new. And the 20th century kept the hits on coming, with tragedy after tragedy laid at the feet of science and reason. We may know now that all of those people made critical errors and overreached with hubris or were outright corrupt, but that doesn't matter terribly much to the person who never understood it well to begin with. All they know is that it's not a sure thing, and it can lead to stupendous tragedy. The tragedies born by anti-intellectualism, such as Pol Pots purging of intellectuals, Maos similar practices that resulted in profound starvation and the deaths of millions, couldn't get much airtime in the face of society shrinking away from reason.
I don't think this is a simple problem. In fact, I have often referred to it as the single biggest problem facing the human species. Civilization includes its own undoing. At the beginning, lethal danger, famine, disease, and other terrors of the past make people willing to try anything - even dispassionate reason. And then they build a civilization. Whose primary, if not sole, goal is to remove danger from the lives of as many as possible. This must, absolutely must, include removing the dangers which motivated the willingness to reason and ignore intuition. Given enough time, arguing for expansion of the infrastructure of civilization becomes harder. Given more time, arguing for maintenance of the existing infrastructure becomes harder. People revert to relying on intuition if for no other reason than it is easier and no longer bears many negative consequences. And when the infrastructure begins to fail, and danger re-asserts itself, it is naive to think people would see the error of their ways and return to reason. There is no historical basis for such a hope. The mother whose unvaccinated child dies of measles does not blame herself. No, they will blame not having gone far enough. They will blame what remains of the infrastructure, and call for it to be dismantled. And they will continue until humanity returns to its 'default state' of slogging through the mud, racked with disease, starving, killing each other over whose god is stronger.
