Actually, it's all about the teeth... All these animals (rabbits, hares and pika) are members of the family Leporidae and of the order Lagomorpha. In older classifications lagomorphs were usually placed in the order Rodentia. Both rodents and lagomorphs are gliriform mammals; that is, they have enlarged, ever-growing incisor teeth that function as effective tools for gnawing. Under this scheme, the lagomorphs were the suborder Duplicidentata, and the true rodents the suborder Simplicidentata. Early workers, however, recognized many features separating these suborders. For one, there are two pairs of upper incisors in lagomorphs (thus the name Duplicidentata) as opposed to one pair of upper incisors in rodents (Simplicidentata). It is now known that lagomorphs and rodents have long separate histories and that even their earliest representatives did not closely resemble one another. Accordingly, it is more accurate and currently generally accepted to classify the two groups as distinct orders, Lagomorpha and Rodentia. (Source: PiedPiper Northern Limited a rodent control company).
Fact is, it hasn't been that long ago, (Gidley, in 1912 removed them from rodents but retained implied evolutionary relations) relatively speaking, that hares (and their cousins rabbits and pika) were classified, however mistakenly, as rodents. It only points up the difficulty in classification of species. I would not have the temerity to speak for Q, however... he's quite capbable of that himself...