Why cannot maps represent the exact size or shape of Earth's features ?

Answer 1

Because maps are flat, two-dimensional objects. The surface of the Earth is not. All flat maps are therefore some sort of projection.

At small scales, the distortion is not noticeable, so the map of your city doesn't appear distorted. But over larger scales, like say continents, the particular projection method chosen can produce funhouse-mirror-like alterations is size and shape.

Answer 2

This is actually a mathematical question. It is impossible to convert the surface of a sphere to an orderly two-dimensional shape. Try to make an orange peel completely flat, and you'll see what I mean!