Aside from the occasional religious nut - the "official" Flat Earth Society answer comes from this page on their Wiki:
https://wiki.tfes.org/The_ConspiracyPersonally - that doesn't cut it for me.
The Flat Earth explanations for the motions of the sun, moon and stars are fundamentally inconsistent with the ways that people used to navigate at sea before the advent of GPS and radio navigation aids.
As recently as the 1940's, people were still navigating using celestial navigation and compass-based techniques - which just don't work if the Earth is Flat. Just look at any FE map and notice how the distances between the continents are very much different than on a globe.
So this "conspiracy" would require ship's captains and navigators to learn how to navigate on the Flat Earth. But all of the books, instruments and manuals that survive from those days talk ONLY about the round earth approach to navigation.
Are we to believe that there were separate SECRET navigational techniques that were taught to hundreds of thousands of ship captains and navigators - an d that not one single one of them EVER revealed that secret?
Perhaps governments who (for some bizarre reason) were sufficiently desperate to keep the flatness of the Earth secret might somehow have forced all of these men into a lifetime of silence...but what about the pirates who ravaged the oceans of the world? They were STRONGLY anti-government agents.
Why would none of THEM ever speak about how there was this secret society of captains and navigators?
This is beyond the realms of reason...and that's true of 99% of Flat Earth claims.
The FE'ers are VERY good at coming up with ideas and explanations that seem right to a quick, superficial glance at what they're saying - but once you dig down into it a bit, it all falls apart into illogic and incredulity.
People who believe in FE seem to be quite lacking in math skills, logic skills, debating skills - and they almost universally are not well-travelled, so they don't see with their own eyes much of the damning evidence.
Look at a crescent Moon in the northern USA, Canada or Europe...then look at it again from the Equator...and again from the southernmost regions of South America, Africa - or anywhere in Australia...and you'll instantly understand why the Earth CANNOT POSSIBLY be flat.