Now according to R’ Chaim the reason why they protested was much more basic – it’s an issur of lo yihyeh kli gever al isha.
Do you really think R’ Chaim is coming to argue on the Kol Bo, and with that to ask a tzorich iyun on the Rema? This is the lashon of the Bais Yosef:
??? ??? ?? (??’ ??) ??? ??”? ??? ??? ????? ????? ?????? ??? ?????? ??? ???? ????? ?????? ????? ???? ?????? ??”? ????? ????? ???? (??’ ?????? ??’ ?) ???? ???? ???????? ???? ??? ????? ?????? (??) ????? ?? ???? (????? ?? ????) ???? ???? ?????? ??? ???? ?? ?????. ??? ???? ???? ??”? ??? ????? ??????? (?”? ????) ????? ??????? (???? ??? ??) ????? ?? ????? ?????? ?? ????? ???? ??????? ?????? ??? ??? ????? ???? ?????? ????? ???”? ??? ???? ????? ???????:
To say that R’ Chaim is arguing is not reasonable.