It’s partly a joke (your favourite peeve, for example) and probably a reference to the other, now archaic, meaning of pet:
fit of peevishness, offense or ill-humor at feeling slighted
I think you can accept idioms as they are or you’ll be endlessly feeling like one saying or another has got your goat
Janeway is a blood-crazed necromancer who obviously lept at the opportunity to kill someone to bring two people back
Good thing they had an organ printer otherwise she’d be chopping people up for their kidneys