As the story goes, I think that the earth is flat in the same way that parallel lines touch.
In our perceived reality the earth is flat and if we travel south we might appear to see a wall of ice. Parallel lines touch because our perspective allows us to see only that much.

The fact is parallel lines don't touch and the earth is round, but it's not shameful to say that you they appear to be so.

Truth is for most of us it doesn't make any difference if the earth is flat or round. Things are sorted out for us already so we don't have to take earth's shape into account for our whole lives. However, when people will have to do something so big that they would have to take earth's shape into account, they will realize for themselves which theory works best for them. If you believe only what you see, go up there and see for yourself.