Why a Flat Earth?
1) Staying on top
Once again, picture in your mind a round world. Now imagine that there are two people on this world, one at each pole. For the person at the top of the world, (the North Pole), gravity is pulling him down, towards the South Pole. But for the person at the South Pole, shouldn't gravity pull him down as well? What keeps our person at the South Pole from falling completely off the face of the "globe"?
2) Falling off
As we begin to make this argument, we acknowledge beforehand that we are aware of the property of matter known as friction. Yes, we realize that whenever two surfaces are held together by any force there will be a static frictional force that will resist any motion by either surface in any direction other than parallel to the force. The example we are using is an extreme situation, and would involve the object in question to travel a considerable distance (tens of degrees of latitude) from the "top" of the planet.
Using the "round Earth" theory, setting an object on the earth would be like setting grains of sand on a beach ball. Certainly a few grains would stay - right around the top, the surface is nearly horizontal - but when you stray too far from the absolute top of the ball, the grains of sand start sliding off and falling onto the ground. The Earth, if round, should behave in exactly the same fashion. Because the top is a very localized region on a sphere, if the Earth were in fact round, there would be only a very small area of land that would be at all inhabitable. Stray to the outside fringes of the "safe zone", and you start walking at a tilt. The further out you go, the more you slant, until your very survival is determined by the tread on your boots. Reach a certain point, and you slide off the face of the planet entirely. Obviously, something is wrong.
1) The fluid problem
Water. Regardless of which train of thought you follow, it covers over seventy-five percent of our planet's surface. And the atmosphere, also a fluid, covers the entire surface. The difference is why. While flat-Earthers know that the ocean is really just a large bowl, (with great sheets of ice around the edges to hold the ocean back), and the atmosphere is contained by a large dome, the backwards "round-Earth" way of thinking would have you believe that all those trillions of gallons of water and air just "stick" to the planet's surface.
Conventional thinking would suggest that the water would just run down the sides of the Earth (to use the analogy again, like droplets running down the sides of a beach ball) and fall into outer space, while the air would dissipate. Using the earlier mentioned idea of "gravitational charge" gives some credibility to the theory. If the fluids were static, then exposure to the gravitational field for a long enough period of time would allow their molecules to align themselves with and be pulled in by the field.
But fluids are not static, especially not in the atmosphere and oceans. Great ocean currents run both at the surface and deep below, carrying water across huge basins, keeping the solution far from stagnant. Jet streams of air travel at hundreds of miles per hour through the atmosphere. And windblown rainclouds carry vast quantities of evaporated seawater across miles of ground, releasing their load far from its starting point. Water or air that (according to "round-Earth" theory) starts on one side of the planet could end up completely on the other side in a matter of only a few days. With all this turbulence and motion, if the world were round, the oceans should all fall "down" into the sky, leaving the planet dry and barren, and the atmosphere would simply float away. Why, just look at the moon. It is round, like a ball, and yet it has no atmosphere at all.