In reality Flat Earthers usually aren’t grounded in whether or not the Earth is flat. They’re grounded in one of two points: the government is lying to them or the government/science people think they’re stupid.
If the government is lying to them, they just disbelieve everything the government says. Republicans did this under Obama, and Democrats are doing it under Trump. It’s the same kind of passion, only even more extreme. The Flat Earthers are just against whatever the government says, and NASA does say the Earth is round. Therefore, the Earth is Flat, QED. It’s not a cosmological theory; it’s a social theory. “Those people are lying!”
The other one is that science people called them stupid, so they just don’t believe anything. People do this all the time. If you tell someone smoking is stupid, the smokers will keep smoking just to show you. This is why people roll coal. A lot of people think sciency types told them they’re stupid, so they just refuse to agree on principle. This also happens a lot with vaccinations and GMOs. Like FE, they sorta feel right if you don’t explore the notion much. Again, social theory not physical.
You can argue physics and explore physics. You can’t argue that someone shouldn’t distrust the government or be insulted by physicists who call them stupid.
Anyway, imagine you have a boat and you go to the Pacific Northwest. You can sail fifty miles out to sea and see the mountains near Puget Sound. But you can’t go thousands of miles out to sea and see them. You should be able to if the Earth was flat. What’s more, again, when sailing east towards Puget Sound, the mountains will appear to rise. IF the Earth was flat, they’d just sort of appear out of darkness. This is not the case. They rise.