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Bats hang upside down because they do not have the capacity like birds to launch themselves into the air from the ground or any other standing position. Basically, by hanging upside down all they have to do to take flight is let go and gravity propels them down fast enough for them to become airborn.
There is a school of thought that maintains that pterodactyls used to climb up trees and launch themselves in a similar fashion. The ones who used to jump off cliffs died out because it took them so long to climb to their launching sites they were devoured by predators along the way.