Why don't people 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.