Why do bats hang upside down?

This is a little like asking, "Why do people walk with their legs?" People could walk on their arms instead, and some people (acrobats for example) actually do it sometimes. But our legs are a lot stronger than our arms, and the whole human body is set up for walking with the legs. Walking with the legs is easy and comfortable and natural. So we usually walk with our legs rather than our arms.

It is the same for bats. A bat's body is set up to hang upside down. In fact, if you look at a bat's legs, they are set up so that, without doing anything, they naturally cling when the bat is upside down. The weight of the bat pulls on tendons that hold the feet closed. So bats hang upside down because it is easy and comfortable and natural for the bat.