Early civilizations thought that the earth was flat, yet they looked at the moon every night. Why did people think earth was flat when the moon was not?
I'm not entirely sure what you mean. The moon is round, but just looking at it doesn't tell you it's a sphere and not a disk.
Relatively few people thought the earth was flat. The Greeks knew it was round and Eratosthenes calculated the circumference to within 66 km before 194BC. It was also visible to less educated people in a variety of ways http://en.m.wikipedia.org/wiki/Spherical_Earth. But for those people who believed only what they saw a pasture or road appears flat to someone relying solely on limited direct observations.