Bats belong to the order Pterodactyl, not the same rodent as the mouse. This is a long-standing cognitive error, as the word “bat” is similar to “rat” in many languages, for example the bat “Fledermaus” means “trembling” and “rat” in German.
Bats and mice are not closely related. In fact, on the molecular phylogenetic tree of mammals, humans and rodents are closer than bats!
So it is a rumor that bats are flying mice.