I think I can share a set of flat earther characteristics with you.
They are unfit people of modern science.
It's about they want to use the flat earth theory to express their hated towards modern science.
There are a part of humans, maybe a lot, they are totally discomfort about we use science to explain the world, they want to use their own fairy tales to understand world, they did it for thousands of years. Until the Age of Enlightenment. Since that, they can't do it anymore.
And they can't change their cognitive function, it's very likely is born this way.
They are quite useless in the modern society. In words of modern society: individuals are very likely to get/got schizophrenia.
Human was had an open mind for their BS(believe the earth is flat) hundreds of years ago, but now, don't have the space, so they are angry.
But they can piss off people like you for bitching, someone can adapt for the worldview of modern science. It's not about they believe the earth is flat or not, it's about talking BS to piss off people.
So you are an obvious target of them.
In my theory, share the screenshot can let him feel like he is totally piece of shit, then he is going to shut up.