Flat earth falls short on many accounts, but the one I want to address here is its mistaking the physical as final reality. This is an error that it shares with more popular concepts, such as heliocentrism (earth going around the sun) and even geocentrism. If one accepts a physical reality as final, he cuts himself off from being able to see that his model is wrong. Models proposed based on physical observation do not establish final reality.
Hebrews 11:3 (KJV)
Through faith we understand that the worlds were framed by the word of God, so that things which are seen were not made of things which do appear.