Yet, when people do encounter flying squirrels in my area of New York’s Catskill Mountains, the animals are often dismissed as pesky attic invaders, and their magic is downgraded to mere nuisance.

Scientists aren’t supposed to use words like “strange” or “strangest,” but Kristofer Helgen can’t help himself. After all, he says, the life of the woolly flying squirrel is “one of ...