A person who coaches, trains, or instructs others in a sport, skill, or subject; a trainer or tutor.
From 'coach' (to instruct) plus '-er' (one who does), a straightforward agent noun that has been in use since coaching became a recognized profession.
Interestingly, the original 'coaches' were horse-drawn vehicles from Kocs, Hungary—then the word transferred to mean someone who 'carries' people forward in their learning, showing how language recycles old words for new concepts!
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