I was asked about the origin of the expression, which usually contains more words to describe a hair that has found its way into a position to make a person behave in an uncomfortable, strange, or unexplainable manner. Blogdom.org believes the saying evolved from the skittishness of hares during the breeding season. It gives the example of Lewis Carroll’s Mad Hatter’s tea party.
Wild hare was used to describe the erratic behavior of rabbits in rut, which then created the expression used to describe behavior that defies explanation.