I have talked to a lot of flat-earthers because of my fascination of crackpotism. Let me say that there are many kinds of flat-earthers, and some of them are more intellectually respectable than others.
The ones I respect the most are the ones that subscribe to what I like to call “empirical-only-skeptics”. These people are skeptical of anything that they do not empirically test themselves - this means that proof of the roundness of the Earth through satellite photos to them are inadmissible. Similarly, proof of conventional gravitational physics (most of them do not believe in conventional gravitation, as gravity equilibrates the flat-earth into a sphere in short timescales) like LIGO are inadmissible.
From this, they either come up with their own experiments or take “experimental data” from people that have no real stake in the globe/flat shape of the Earth and devise their own conclusions. It is very applied-scientific-method-y and I respect them for doing this.
Now, the problem is that these flat-earthers are typically more knowledgeable in physics than the average people, at least knowledgeable enough to ask probing questions about mainstream physics, but not knowledgeable enough to properly answer them.
Indeed, I think if I ask a class of physics undergrads to debunk some of their arguments in ~1-2 classroom periods, I expect that more than half would fail this test.
This feeds into another problem, which is that people who come to debate them usually both have no real physics education (their arguments usually boil down to: flat-earthers are wrong because so-and-so scientist or textbook said so), and they come in swinging with an extremely arrogant attitude. These people are typically outmatched by the flat-earthers, which feeds their ego and make them more entrenched in their idea.