The point is that your FE maps actually claim to be representative of the Earth's actual shape, when in fact, they are not. REers to use flat maps, but none of us pretend that that represents the true shape of the Earth. And why do we use flat maps? Well, primarily because you can write on them, and because you can fold them up and put them in a pocket. Using a globe that is large enough to write upon for navigational purposes would require quite a large one. Such large ones are made, but they are still impractical for writing on, just for the simple reason that writing accurately on any three dimensional surface is difficult. So it is far easier to transfer the surface of the globe to a flat, two dimensional surface.
However, the fact that we recognise that that the world is a sphere is clear by the fact that on world maps in the Mercator projection, Asia is often split in halves. You can find half of it to the West of California, and the other half to the East of Europe. This is done for two reasons. One is simply cultural vanity. Europeans and European Americans like to put themselves in the middle of the map. The Chinese still call their country Zhonguo, the Middle Kingdom, with a similar level of vanity, and they, incidentally, believed the world was flat up to the XVIII Century.
The second reason is, however, more practical. That is the fact that if you take a paper map that is designed in the above way and bend it around into a circle, you get Asia touching itself, which is what it actually does. So, on a Mercator map projection, recognising the world is round, you can circumnavigate the Earth at the Equator. This cannot be done on the bipolar map. The unipolar map presents yet other problems, previously spoken of, particularly when travelling South of the Equator.
Again, I suggest, that Flat Earth folks have a serious problem on their hands. One, they cannot present a map that all FEers agree with. Two, even when you get a map that some agree with, it is so invariably flawed that it cannot be taken seriously. That is the fundamental problem. If you don't even have a valid map of the Earth, what have you got?