Using unhelpful skepticism as a reason for hiding the fallibility of science will produce more generations of people that believe whatever the scientists tell them, which at times will be wrong and yet accepted by almost everyone as truth.
I think the primary problem is the inability for most people to self reflect on what they know, and most importantly, whether they even know it at all, to critically evaluate their assumptions about the universe and the extra meta level of how they came to those assumptions. It is painful to mercilessly question yourself and your entire belief system and in today's world it is probably harder than ever to build a coherent picture of reality due to increasing noise and complexity of ideas.
I'm not suggesting that, I'm suggesting a de-emphasis on framing it as a matter of "science" and leaving folk wisdom and all other assumptions of perspective and "trusted sources" untouched.