Some people try to adjust their opinions by getting pieces of information and considering which ones fit and which ones don't within a (more or less) rational frame.
In contrast, everyone has their opinions biased by what they repeatedly hear others say. And if they "like" what they hear, the story, then almost everything is lost.
But it's not just "don't let the facts get in the way of a good story", it's more like there's a lot of people who is incapable to see that some pieces simply don't fit together. They understand what a contradiction is, but it can't reach their eyes when there's a story that already shines more brightly for them.
Not a lot of people believes they "can reason about complex systems based on their gut feeling". That's what you see they are doing, but that's not how they think about it. They simply see a bright light, and call it understanding. You are only pointing at dimmer lights beyond their blindness. First, you need to teach them how to put pieces of information together in a field where they aren't blinded by a nice story already. Then, they have to start applying their newly found rational thinking to other areas where their gut/irrational/random feelings are stronger, until they see that those are very fallible.
No one has so much time though, so we shall continue giving them flak and trying to become great preachers on HN instead.