I think that the Flat Earth Society is just an extreme example of where a certain type of attitude and thinking (possibly caused by mental illness) can take you.
There’s first the anti-science aspect of it. We see elements of that to at least some extent in denial of evolution, denial of anthropogenic climate change, the anti-vaccine movement, and the anti-GMO movement. Heck, even groups not inherently wrong may have their pseudoscientific fringes (e.g. vegetarians).
Then there’s the allure of being privy to some secret knowledge about lies that have duped much of mankind. Not only does it appeal to one’s pride, but it also often ends up creating some clear-cut evil that’s separate from one’s self and is theoretically defeatable, perhaps with the knowledge that the person possesses. Even if not, there’s the sense captured in Helloween’s song Kill It: “People never wonder how the world goes 'round. They who know must follow. They who don’t die bound.” Ramblings aside, we even have people who have made careers out of duping these people.
And finally there’s the people who almost seem to think experience and knowledge are a sign of proud elitism. This of course contributes to the above two (sort of ironically when you think about it). I myself was even called “condescending” because I had the nerve to point out to someone that I was speaking from first-hand experience and they weren’t.
Overall, these factors can lead to weird places. It may not always lead to Flat Earth Society levels of…pitiful…but I’m pretty sure if you spend enough time around these forums, you’ll find the same elements around here just coming to less extreme conclusions (normally).
Edit: I realize now that this post is a bit serious for Casual Discussion, so here’s a funny picture to lighten the mood: