In spite of rational power of mind, on which all modern civilization has been built, it is often forgotten that human nature is deeply irrational and that the dark side of it might be a serious obstacle in solving some of the most important challenges of contemporary time. That explain why, in the era of scientific-technical civilization, there is a paradox of an enormous irrational distrust and fear of science and rejection of its recommendations concerning burden against the coronavirus pandemic. In this article it is considered why irrationality is still so powerful and what could be done to change it.