I think it’s meaningless because it doesn’t really achieve anything for the woman.
But that is a different argument, and one worth having. I was responding directly to your statement that it was meaningless because of cultures where man is seen as the head/patrimony.
But if all a man does, with regards to women is open doors, pay for dates, etc and beyond that sees treates them with a lesser dignity, then I would agree, in those instances they are meaningless behaviors. But that does not mean, in general, they are without meaning.
Allow me, if you will, to take your homeless analogy and describe an actual conversation my wife once had with a woman. This lady told her, at one point in her life, when she had two kids at home and no means of support, she was actually begging on the street for help. She said the very worse part of the experience is how people would give her money, but that was it, they would not even make eye contact with her. They simply wanted to get away from her as fast as possible. This really struck home with me, because I am a person who tends to give money to beggars, but I realized that I was 100% guilty of the behavior this lady described. Since then, I have always made a conscience effort to look at them, and say something, perhaps just a" God Bless You", or “I will pray things get better”, but to actually interact in someway so that they do not feel like I consider them less than human. Why do I say this anecdote? Because if all I did was way “God Bless You” or whatever, to them it would be just as you say, rather meaningless. But if I do something to help them along and I make such a gesture, I can tell you their response is quite difference than if I just help them along.
So, I am by no means saying that women should not be treated with respect and dignity in all ways, that women should not be treated professionally the same as men with regards to pay and opportunity, that women should not be given authority in the home, that men should not do their share of the housework, etc. I am saying all of these things should be a given (I realize they are not), but women should also be shown these special manners, in addition to all of that. We men, should consider ourselves at the service to women. Why? because they are women. No other reason than they are due it because of their femininity.
I am further saying that teaching boys these manners and behaviors most certainly does not lead to showing them less respect in other ways. Back to our homeless example. It is possible, I suppose, that someone could make a habit of “patting him on the head” or saying “God Bless You” and just walking off, but I think it very unlikely. I think it much more likely that if one starts to physically interact with them in small ways, one is more likely feel the need to do something to “help him along”.