I am no Posek, but the idea that a man should not walk behind a women almost certainly is TOTALLY irrelevant when just walking through a doorway. It means that in the street, a man should walk in a path that is not behind a women. No one said that a man has the right to be rude and not hold the door or jump into the doorway first. To think that Chazal would tell us to do something rude is unconscionable. It is warped thinking and if that is how the fellow will be, let someone else have him as their husband – you don’t want to go near such a person. The ways of the Torah are “Darchei Noam”. The Gedolei HaDor always truly knew/know how to be gentlemen above everything else.
Menu