Why believe a book written by people who thought the earth was flat?

The fact that the authors believed the earth was flat means that they did not have the benefit of divine inspiration, as was once supposed. In theory, the book could still be believed even if the authors had no true knowledge of God, but this very fact must alter our perception of the Bible.

Believing the Bible becomes an act of faith, and no more than this.

It would be safe to say that the authors of that book cannot be taken seriously.

The authors of this book knew more about the world than early scientists. The book of Job says He stretcheth out the north over the empty space, he hangs the earth on nothing.Job 26:7. Astronomers recently revealed that the area to the north of the axis of the earth is almost empty of stars in contrast to other directions. Ecclesiastes 1:7 says all the rivers run into the sea, yet the sea is not full;to the place from which the rivers come, there they will return again. Scientific studies proved that most of the water that forms into the clouds worldwide comes form the evaporation of the waters found in the oceans. Ecclesiastes 1:6 Says: the wind goes toward the south, and turns around to the north; the wind whirls about continually and comes again on its circuit. Three thousand years ago, the writer of that book, King Solomon knew that the planetary winds follow a circular pattern from south to north and south again, which is a fact. Once again, I respond with Biblical knowledge which is so so lacking in the intellectual. The Bible is where the true knowledge and wisdom are. READ IT.

The same reason that they believe that the earth is the center of the Universe, Psalm 93:1 the world also is stablished, that it cannot be moved; Psalm 96:10 Say among the heathen that the LORD reigneth: the world also shall be established that it shall not be moved. And that the waters on Earth is divided with the waters of heaven by a firmament. In other words, thinking is a hard task, so they allow others to think for them..

Another Answer:

It is a logical fallacy to disbelieve something because of an idea that reigned in that particular era. As an example, following the logic of the posed question, why should we believe algebra? Diophrantes, the "Father of Algebra", was an Alexandrian mathematician who lived in the third century A.D., a time when the world was not only thought to be flat, but also the center of the solar system.