Having sharp points that stick out, or easily annoyed and irritable when talking about someone's personality.
From 'prick' (a sharp point) plus '-ly' suffix; 'prick' comes from Old English and Germanic roots meaning to pierce or puncture.
Porcupines and hedgehogs are prickly not to hurt you but to protect themselves—it's a passive defense system that works even when they're sleeping or running away.
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