The adjective hare-brained usually refers to a plan or action that is unexplainably preposterous.
If there is any confusion about this word’s meaning, it lies in the sixteenth-century dual spelling as both harebrained and hair-brained.
In any case, the word is a reference to the wildly odd mating season practices of hares, which are so bizarre that they are the origins of the expression “mad as a march hare.”