And that modern man's self-assessment is largely irrelevant to the functional question.
This is why:
The two are not exclusive; to presume history is detached from the present is insupportable in general.
More particularly, contemporary misogyny is not detached from history; given unbroken male supremacism in our cultural arc at least since the Biblical age, and pretty much observable so far back as the historical record can offer us any insight on the question, we must consider the elements from which any idea or concept is fashioned. That is to say, chivalry itself arose from a misogynistic cultural stew of contempt for, and ingrained prejudice against women.
It sounds like you're asserting that the sins of the father are visited upon the son. i.e. a modern male is to be held responsible for the history of chivalry.
And there really is no way to avoid presuming against women; chivalry is a frame asserting to define a woman;
But now you're getting into what it means to interact with the human population. We look for companionship even while going about our daily lives. Life
is the forum in which we seek companionship. It would be great if a flag went up worldwide that said 'now it is time to socialize' but that's not reality. People looking to make friends or more with another person is part of society. No one who steps into a public place has the right to say "I
never want to be seen as approachable." They
do have the right to say "I do not wish to be approached now. Go away." or "You should know that this is a place where it is not appropriate (perhaps, the workplace)."
So, yes, both men and women, by their presence in public, are allowing themselves to be interacted with - in an acceptable fashion (such as holding a door open for them).
Any person who agrees to be part of society also agrees to accept a certain base level of interaction when in public. "Hi. I noticed you. Did you notice me?"
And to put a fine point on it: your comment"chivalry is a frame asserting to define a woman;" is too specious. It is gender-agnostic and orientation-agnostic.
A straight man may hold a door open for a woman.
A gay man may hold a door open for a man.
A straight woman may hold a door open for a man.
A gay woman may hold a door open for a woman.
They are
all "asserting to define the gender of a person to which I am oriented".
liberating within chivalry is about as inherently contradictory as liberating within marriage―either proposition defines women according to an external template of expectation. But, yes, there was a period of my life in which "women's lib" was expected to feel grateful that women were being graciously permitted more existential liberty within the context of marriage; disappointingly, it actually was kind of a step forward.
]The "modern man who simply delights in seeing a woman smile at him"?
Nobody said anything about expectation or job. It is human interaction: I hope for a smile.
That is not for you to judge.
Chivalry? He could try treating her like a human being instead of some mythical alien creature to be impressed and won over. The smiles he gets from other human beings will be worth far more than coy shadows passing well enough to get through the moment of someone deliberately trying to charm her.
It is not up to you to decide what he could do or what he might gain. That is up to him, and not open for judgement.
It is also not up you to decide whether she appreciates it. That is up to her.
Nor is it your place to decide that being "nice to someone" is contrary to "treating her like a human being" or that being nice is instead treating her like "some mythical alien creature to be impressed and won over". That's just rhetoric.
The day women actually achieve equality in human societies, yes, we will have every reason to revisit our fundametnal comprehension of the relevant social dynamics in order to account for the new reality, but until then declaring some magical transformation of historical misogyny is pretty much ... er ... ah ... the nearest to an excuse anyone can come up with?
We are part of society in the-here and-now. We are creatures of companionship. These interactions are within the normal bounds of societal interaction.
You are beginning to preach. The above is not making any case, it is simply judging something you don't like.
The point remains that modern chivalry is a form of sexism that does not involve dislike or contempt.