Question

Why are all maps distorted?

Answer 1

In simpler terms, you can’t use a rectangle to perfectly map a sphere. If you try and wrap a piece of paper around a basketball, you won’t get a perfect model of the basketball. So you either need to fold the paper/make changes to try and make up for the missing sections.

Answer 2

Because you can't display 3D surfaces perfectly in two dimensions, distortions always occur. For example, map projections distort distance, direction, scale, and area. Every projection has strengths and weaknesses. All in all, it is up to the cartographer to determine what projection is most favorable for its purpose.