Why do we use wide or long lenses?

One reason is to change perspective, as you all know if you read this site.

Here’s another illustration. I took a happy shot of a student yesterday, with the lens set to 24mm (apparently my courses can be fun):

When I pull back and zoom in, to use a 70mm lens focal length, look at the student in the background:

Much larger. Because the relative distrance between foreground and background is greater.

It is the vantage point that creates the different look, not the lens length per se. The wider the lens, the closer you get, and hence, the smaller the background will look.