the very fact that some people are so worked up about this issue as to spend hours posting against Flat Earth says a couple things:
1) that there's something to it
2) they are deeply invested psychologically in the outcome
Otherwise, if it was just craziness and idiocy and it didn't threaten them, why would they spend so much time on it? If some guy posted on here that Joe Biden is a purple alien in a fake skin suit who comes from a race on Alpha Centauri, people may just say "ridiculous" and move on, and would certainly not spend hours debatign it. You wouldn't waste your time and you wouldn't care what some nutjob said.
I think that depends on who the person is. What if you knew someone who was not only a normal, functional and sane human being, but also was intelligent, well-read, highly educated, and had extensive experience with the world, who believed what you described? Especially one with a job and a house and a family and every other indication of being a grounded human being? In that case I bet you would waste a lot of time trying to get into such a person's head, to see how such an otherwise capable person could think something so bizarre. Because it really would then be an interesting question, why does this person have such a strange belief? What convinced him of this?
I have spent 10x more time examining the flat earth idea in the last year or so, since it went viral on this website, than I have in my entire life. I examined the arguments for the flat earth hypothesis with an open mind because it does not impinge on the Faith either way, and I already have enough ideas that are considered looney by the modern world that I have little to lose in terms of my reputation by adhering to one more stranger idea.
It would take me too long to give a complete account of my experience, and I've talked about this on other threads, so I'll try to hit a few high points for now.
First of all, the vast majority of flat earth videos are attempts to argue against globe earth rather than promote their own position. This is a problem because anyone can try to poke holes in some other theory without advancing an alternative position of his own. That is very easy, and any child can do it. But as soon as one proposes an opposing view, then immediately he is liable to being put on the spot. This is a constant pattern.
For example, they spend lots of time arguing against the globe map by talking about plane flight paths, but when someone asks them what they themselves think the map of the earth looks like, they don't have the slightest interest in the question at all, and their answer often amounts to "Who cares?" Whereas if they really believed the globe is a big hoax in terms of the shape of the earth, you'd think any rational person's first reaction would be, "If the earth's land masses don't look like how they are shown on a globe, then what DO they look like?!"
This pattern is even more striking when you talk about the sun. If they think the sun isn't rotating around the globe of the earth, you'd think their first priority would be to figure out what, then, it is doing up there and how. But no, all they do is say casually that it is somehow magically floating in the air, suspended in space, defying the universal attraction of all things downward to the surface of the earth. Not only that, but it is somehow propelled across the surface of the earth. What propels it? Most of them don't seem to ever have thought of the question at all. Then again, they claim it moves in a circular motion. This again is impossible, since any object we see moving through the air moves in a straight line, at least in the atmosphere of the earth. They can't even claim some gravitational pull makes it rotate somehow, since they reject such. But the weirdest thing is not so much that they don't have a way to explain even the most basic components of their theory, but the way they don't even see the need to do so, even when challenged on these things by globe earthers. They can only make statements like, "Just because I don't know doesn't mean the earth is a globe." What?
This irrational manner of thinking is explained in part by their obsession with NASA and the American government, and their apparent belief that the globe model of the earth is a conspiracy promoted by NASA, instead of being the universally accepted belief of western civilization going back three millennia, including the belief of the ages of Faith.