Here is a first convincing argument against the spherical shape of the earth: If the earth were really a sphere, there would have to be regions where it is daytime while elsewhere it would still be dark. After all, a light source like the sun cannot illuminate the entire sphere at the same time.You can easily check this yourself with a flashlight and a small ball: While one half of the ball is brightly illuminated, the other is in the dark. Now imagine how this supposed globe rotates on its own axis: As a result, the boundary between the light day side and the dark night side should gradually move across the globe.