Why does meditation ask you to focus on your breath?

Simply because you have it always handy.

You can focus on your breath whenever you want, wherever you are. You have no excuses; as long as you can breathe, you have something to focus on, and so you can meditate.

Funny how even in pursuits as lofty as the search for enlightenment, the best tools to get the job done are the ones that are most easily accessible.