It's because many Flat Earthers trust only their eyes (they place too much emphasis on the face value of what they see with their eyes) and do not reason about their observations, preferring to take the "simple" route of taking their observations at face value, and discounting more esoteric ones like the Coriolis Effect, Foucault pendulums, the amount of IR radiation reaching the poles, conservation of energy, slight discrepancies in triangles on the Earth, variation of gravity with latitude consistent with a spinning Earth, nuclear fusion, the stars around us, GPS, inertial navigation systems, satellites, and countless other reasons that have been beat to death.
The primary problem is that if a sphere is large enough, any "small" (on the order of a few miles) section of it is very close to flat. This means that the observations that differentiate FE from RE are also very subtle and hard to see unassisted, and need rigorous experiments to prove. It's very hard to see them with eyes if you can invoke "distortion" or "perspective" to discount very small deviations from what would be expected on a flat Earth. If one also has misconceptions about basic physics, then it's easy to come to the wrong conclusions.
Because none of the observations mentioned above affect us in a direct, tangible way, it's hard for people to take them seriously. I believe that this is the reason "Zeteticism" rose out of the scientific method; because people couldn't understand the reasoning and processes behind a lot of scientific observations, they thought that modern science had departed from the core of the scientific method -- observation, hypothesis, experiment, revise hypothesis, experiment further -- by using theories, that while verified to death, seem very unintuitive.
I'll illustrate with one irrefutable observation given by Round Earthers and show how Flat Earth people can muddy the waters enough (and not in bad faith, but to themselves as well) to discount the observation.
RE: If the Earth were flat, you could see the Burj Khalifa from Kansas.
FE: No, because of (1) refraction/particulates in the air that blocks the light or (2) perspective. The first is enough to convince people who don't know why refraction happens (actually, I'll admit that I don't know much about why it happens) or how to calculate refraction on a basic level (Snell's Law), but then one realizes that if refraction is based on the optical density (dependent on many factors, including temperature) of air, there's no reason for it to go only one way. If in certain conditions you can't see the Burj Khalifa because of refraction, then it should also go the other way and you should see more of it. Now to address perspective: to the naked eye, it appears that objects "merge" with the horizon, just as the perspective hypothesis predicts that they will. However, if one takes a telescope/binoculars to view the object, then it's obvious that the object is actually disappearing under the horizon. But it's very hard to reconcile this with the intuitive observation that this is due to perspective.
Do you see how easy it is to come up with and abuse the misconceptions about geometry/physics? How long of an explanation is required to debunk the hypothesis? To someone uneducated in the sheer complexity of modern engineering and physics, it seems far easier to just assert that the explanation is false than to accept that the intuitive observation is false. But when one ponders the issue for a long time, as scientists have done for centuries, one realizes there is no way to reconcile the FE hypothesis with certain observations and There is no reason to discredit the provided explanation for the intuitive flatness of the Earth.