From The Propaganda Professor:
Another popular traditional misconception is that Columbus encountered a lot of resistance to his proposed explorations because most folks at the time believed the earth was flat, and he would just sail off the edge of it. (Into what?). Not true; the rotundity of the planet had been common knowledge since at least the ancient Greeks. There may have been a few people who believed it to be a big platter floating in space, but probably no more than there are today.
The myth of widespread flat eartherism didn’t even gain traction until about two centuries after Columbus, when Protestants made such an accusation against Catholics. In the Nineteenth Century, the myth was advanced further by a handful of scientists in not particularly scientific books aimed at making creationists appear even more backward than they really were.
But for the myth relating specifically to Columbus, we can thank Washington Irving of Sleepy Hollow and Rip Van Winkle fame. His 1828 book A History of the Life and Voyages of Christopher Columbus was the literary equivalent of a 1950’s Hollywood biopic, giving Columbus the Parson Weems treatment. Weems, you may recall, was the “biographer” of George Washington who took great liberties with the facts in order to exalt his subject, and may have invented the cherry tree episode . Similarly, Irving inserted an account of a meeting between Columbus and a Spanish commission to consider his proposed voyages, in which the commission objected that the silly navigator believed the earth was (snicker, snicker) spherical, and they couldn’t possibly get behind such a notion. The meeting was apparently real. The objection was not.