That was ignorance and superstition among the uneducated classes, dear. ;)
What the serfs and artisans thought was beside the point. It was the merchant lords, and the kings and dukes, that could foot the bill for a voyage.
And why should they? They were after money and power. Exploration for its own sake was silly, and sometimes heretical! Science had to wait until a scientist prince came along. Helllloooo, Henry the Navigator! Columbus got his commission because he promised a shortcut to a very lucrative market that Henry's initiatives had already opened for Portugal. They knew the world was round already.
I like the Bugs Bunny cartoon, though:
Columbus: The world, she is round-a, like-a da meatball.
Ferdinand: The worl', she eez flat, like dee tortilla.
Inaccurate history is some of the most entertaining history there is. :)
The Greeks knew the world was round from geometry, and the Romans knew from them. The Arabs knew from the Greeks as well, and Europe knew again for sure by the 1500s, when Greek learning was rediscovered and publicized with that new-fangled printing press. Europe's educated classes knew long before that, because Greek learning was still on life support inside the monasteries during the Middle Ages.
In the meantime, the Polynesians and the Vikings hadn't exactly stayed home, either, but they had vessels that would stand up to the great oceans instead of galleys designed for the great inland seas.
Once Western Europe looked out toward the Atlantic, instead of inward toward the Mediterranean (the end of which habit we can thank hostility with the Muslim kingdoms who controlled the Silk Road for), it was a whole new ball game.
It wasn't principle that kept people home. It was commerce.
Kind of what keeps us on Earth instead of establishing extraterrestrial outposts, huh?
Regards--
Mary Anne