This is a nice fantasy but it fails to a number of intractible social problems. Children aren't taught skepticism because parents don't want their children to be taught skepticism. You would need to use force that you do not have access to in order to even attempt the solution you are proposing.
Second, implicit in your argument is that people would be responsible for thinking critically about every fact that they believe. This is just too much work, the human strategy requires trust, and we have massive incentive structures called societies whose main job is to facilitate that trust through the establishment of systems of incentives. This complicated system of incentives has been demolished, wholesale, by social media, and we're not going to adapt fast enough to avoid serious damage.