why is there so much branching in the lungs?

Answer 1

It increases the volume of your lungs.

Answer 2

It increases surface area of your lungs. Think of your closed fist and knuckles as a membrane so 3" of surface area. Now open your hand and spread your fingers. Now in between your fingers is more surface area than before and more area to exchange things across. That is the easiest explanation for increased surface area I can think of.

Answer 3

Each tiny branch must end in an alveolus or air sac. We have to have many, many of these air sacs in order to have enough surface area to exchange carbon dioxide and oxygen.