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.
It does when it's in free fall.
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.
Why do you think this is true? Do you believe that once you leave the surface, your momentum immediately vanishes? It doesn't.
Curvature- Where is the curvature??
Here's an example. It's a photo of Chicago from across Lake Michigan. It was initially presented on these forums by a flat-earther.
In it you can see only the tops of the very tallest buildings. Where is the rest of the Chicago skyline? It is behind the curved surface of the water.
The list goes on and on...
How come you omitted:
Sunrise. How does that work?
Sunset. How does that work?
Circumpolar stars around the northern
and southern celestial poles, but the separation between the stars in the sky doesn't change. How does that work?
The horizon. How would that happen?
Oh, yeah... those are all easy to with a spherical earth, not so much if the Earth were flat. No wonder you "forgot" to ask about them.