I would like to find the way to explain in an easy manner why we write "butcher's, doctor's, dentist's, greengrocer's" with the final "s".
Any idea how to explain it?
I think he means why don't we just say I went to the doctor, the butcher, the candlestick maker....
And I guess the answer is it's more polite to describe visiting the place belonging to the person than the person himself.
Cf. in French: we say chez le médecin, chez le boucher.... also a form of possessive in a way.
It's a short way of saying the butcher's shop, the hairdresser's salon, the doctor's surgery etc.