There is no logical proof or even explanation. It is just extremely childish and ridiculous. There is no reason to believe in the Earth being flat.
To me the illogical thing would be to believe the world is round, and most rational adults would reject the idea if they were not taught that Earth is round since kindergarten. The RE model goes against everything we observe in our daily lives and we have gone through them all many times such as:
Gravity- Water doesn't cling to a ball. Somehow this pretend force is all around us and keeps the entire universe perfectly in order.
Rotation of the Earth - If the Earth is rotating then flights going the opposite direction of the rotation should take less time than those going the same direction.
Curvature- Where is the curvature??
The list goes on and on...