The thing to keep in mind, perhaps, is that most people who are convinced that the Earth is a sphere don’t actually know why, for sure.
Some flat earthers find the idea is appealing for religious reasons, others are of the crowd who think NASA is evil, space a fake, and the moon landing didn’t happen. But mostly it’s because they think they are merely being rational skeptics. They have not themselves been able to prove the earth is round, so they believe they are only reasonable when they request evidence. CNN for example reports from a flat earth conference: “Like most of the speakers at the event CNN spoke to, he was convinced after he decided he couldn’t prove the Earth’s roundness.”Sabine Hossenfelder, “Flat Earth “Science”: Wrong, but not Stupid” at Back(Re)Action
I want to leave aside here that, of course, you cannot strictly speaking prove any empirical fact; you can only prove mathematical identities, so more precisely we should speak of seeking evidence that disfavors the hypothesis that the earth is flat. Of which there is plenty, starting with the historical evidence about how stellar constellations shift if you travel, how the length of shadows changes, to Newton’s 1/R2 force law that is the law for a sphere, not a disk, not to mention Einstein and gravitational redshift and the perihelion precession of mercury, and so on, and so forth.
The problem that flat earthers have is that they cannot do most of these observations themselves. So if you buy the idea that it’s only your personally collected evidence that you should accept, then it seems you cannot refute the idea that the earth is round, and so flat earthers philosophy forbids them to accept scientific fact.Sabine Hossenfelder, “Flat Earth “Science”: Wrong, but not Stupid” at Back(Re)Action
Let’s keep this info handy if we encounter assertive flat-Earthers. Hossenfelder adds,
It is not possible for each and every one of us to redo all experiments in the history of science. It therefore becomes increasingly important that scientists provide evidence for how science works, so that people who cannot follow the research itself can instead rely on evidence that the system produces correct and useful descriptions of nature.Sabine Hossenfelder, “Flat Earth “Science”: Wrong, but not Stupid” at Back(Re)Action
Well, she does a pretty good job herself.