I agree with you; it's a complicated subject. But just know that the informed and scientific community all unequivocally know that the Earth is round; I applaud you for listening to our arguments. I'll repeat it again. The Earth is round. FE has resorted to denying basic, proven science, such as the Lawson criterion for nuclear fusion, the existence of gravity, the laws of optics, and the functionality of rockets.

the_random_one, the Earth looks flat to you because it is so large and you are so small. To see what I mean, imagine a massive sphere, or walk up to a spherical sculpture like this one:

http://2.bp.blogspot.com/-_8NVovlkZfc/VIugTnpPYdI/AAAAAAAA0kY/ZyegjsosTbk/s1600/ball2.jpg. Now take a marker and draw a 1 inch by 1 inch square. This is what you and everything you can currently see are like on that sphere. If you imagine cutting out that square and laying it on a table, you'll see that it is awfully flat. This is the same reason why the Earth looks flat to you; because you only see that 1 inch by 1 inch square.

If you want a more mathematical treatment, I wrote about this in the Occam's Razor thread (sometimes these threads get derailed by wrong math):

I'd like to also include a bit of mathematical intuition for the seeming flatness of the Earth. Imagine you are standing on a large perfect sphere which is the Earth. It looks like the Earth's surface is flat because you can draw very straight lines on the surface. The Christoffel symbols of the second kind for spherical coordinates (note: this is the same coordinate system we use with latitude and longitude; the radius is fixed) are given at http://mathworld.wolfram.com/SphericalCoordinates.html. As we all know, the Christoffel symbols vanish (become 0) in Euclidean space (that is, a coordinate system in which we can draw straight lines). Now consider movement on a very large circle (r=6400 km). Even if you move a seemingly long distance on your scale (say 10 km), you will move a very small angle. Extrapolating that to spherical coordinates, we can conclude that both theta and phi are very small in the local (that is, near you) coordinate system. So in the local slice of the spherical coordinates, you can see that all of the Christoffel symbols are incredibly small because the radius is large and the angular displacements small. This means that your local coordinate system is very similar to a Euclidean space and therefore the Earth seems flat.

TLDR: If you take a small section of a very large sphere, it looks flat. I wish I had a nice GIF for this, but I can't find one.