At least in some places I've lived, that kind of courtesy--shown by a woman to a man--would likely get her an unwanted come-on. So the woman won't do a courteous favor for a man she doesn't know (at least, a man of the age group that most frequently hits on women they're not acquainted with).
Similarly, if a panhandler asks for change and I at least acknowledge his existence--giving him a smile and a shrug, indicating that I don't have any to spare--more often than not I get a pleasant word and a smile in return.
A woman who did the same thing would probably get hard words in return, so the woman can't acknowledge the panhandler's existence as a human being. She has to pretend he's not there, ignoring him completely.
That kinda sucks, but it's the reality...