Why do mapmakers have to choose between showing the correct land shapes and distances on the earth?

The mapmakers have to make this choice because of the shape of our planet and because there is still not a method as to how to have both the land shapes and distances to be precise at the same time.

The shape of the earth is the factor that is not allowing (at least for now) that we have both correct land shapes and precise distances on the maps of the Earth. Because the Earth has a rounded shape, as we move further away from the Equator, the shapes are deforming more and more, or rather they are stretching more and more which makes them appear much bigger than they actually are, thus giving us an unrealistic picture of the size of some of the places on our planet.