Do you pet your pet because it is a pet? Or is it a pet because you pet it?
I can answer this.
Pet, noun: “tamed animal,” originally in Scottish and northern England dialect (and exclusively so until mid-18c.), of unknown origin. Sense of “indulged child” (c. 1500) is recorded slightly earlier than that of “animal kept as a favorite” (1530s), but the latter may be the primary meaning
Pet, verb: 1620s, “treat as a pet,” from pet [above]. Sense of “to stroke” is first found 1818.
So: you pet it because it’s a pet. It’s a noun that was verbed, rather than a verb that was noun’d.