Origin of harebrainedfrom obsolete hare-brain, heedless person, one having a brain like a hare's + -ed
An example of something harebrained is a plan that has no chance of working.
Usage Note: The first recorded use of harebrained dates to 1548. The spelling hairbrained also has a long history, going back to the 1500s when hair was a variant spelling of hare. The hair variant was preserved in Scotland into the 1700s, and as a result it is impossible to tell exactly when people began writing hairbrained in the belief that the word means “having a hair-sized brain” rather than “with no more sense than a hare.” While hairbrained continues to be used, the standard spelling of the word is harebrained.