Why don't people listen to smart people? Generally speaking, I feel like there are two things everyone can agree on when it comes to intellectuals:


They don't know everything.
They know more than me (at least about a particular topic).


It's #2 that's tripping me up. The words of a Know-It-All are usually very poorly received (at least in Western culture). We don't consider intelligence as a meaningful criteria for political office, we bully them in schools, and even tell them to their faces that they're wrong about scientific/mathematical concepts that we admit to not understanding! When a problem arises in our lives, they are the last people we want to hear from. We instead run to the counsel of our family, friends, and other people who many times know even less about the problem than we do!

But why? Everything we have as a species is owed to our brains. If they really do know more than us, it would be in our best interest to revere them, no?

Have there been any studies done that would explain why people generally don't listen to smart people?
David Dunning and Justin Kruger have observed that, related to skill competency, individuals which are incompetent in a certain skill can exhibit a cognitive bias, called the Dunning-Kruger effect, which leads them to:


fail to recognize their own lack of skill
fail to recognize genuine skill in others
fail to recognize the extremity of their inadequacy
recognize and acknowledge their own lack of skill, but only after they are exposed to training for that skill


While the study focuses exclusively on why people can or cannot measure their strenghts and weaknesses correctly, there was an interesting subsequent study where the authors were lead by the fascination that certain incompetent poor performers fail to ever improve. They have concluded that such individuals have an apparent lack of self-insight, which leads to exhibit incorrect logic and defensive mechanisms which fixate their views even against continuous feedback and encouragement to improve.

This certainly remains a complex phenomena which we could, from experience,  observe in different forms. Based on the suggestions from the last study, it seems that this becomes an issue with individuals that have not conceived intelligence as being malleable. Apparently, they may not have been instilled to value intelligence and encouraged to approach learning and the refinement of it's processes for the betterment of one's own intelligence as an endeavor which is to be considered as rewarding.

Effectively, being that they consider intelligence as something that is fixated, failing to generate excitement when they engage others that attempt to challenge and broaden it seems to lead to the difficulties at hand, such as: I do not understand you and I am certain I never will, so I choose to continuously ignore you because I do not want to feel this discomfort that arises from knowing that I am invariably incompetent, which you and I both know is not a good thing.