To make fun of or provoke someone playfully or mockingly, or to gently pull apart fibers.
From Old English 'tæsan' meaning 'to pull apart, card wool.' The sense of 'annoy playfully' developed from the idea of pulling at someone like pulling apart fibers.
The word 'tease' originally meant combing out wool fibers - the playful annoying sense came from the metaphor of 'pulling at' someone the way you'd pull apart tangled wool. Hair 'teasing' for volume uses the original textile meaning!
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