More like everyone did.

The myth that people thought the earth was flat has been attributed to Washington Irving (late 18th/early 19th century author & historian).

Columbus actually thought the earth was pear-shaped and 1/3 of the size that everyone since the Ancient Greeks knew it to be.

The issue was not "we'll fall off the edge of the earth." The issue was "Holy cow, you're going to try and sail 13,000 nautical miles?"