Chivalry is not about treating other human beings with gentleness and respect.
Not "other human beings" — the knight was pledged to protect the weak and defenseless ("women and children first") and to value the honor of women, which meant treating women with gentleness and respect.
The lady is one of the most hypersexualized figures in Western Culture.
is also an obsolete, now functionless, concept.
She is pure. She is innocent. She is chaste. She is fragile. She is to be put on a pedestal.
Yeah, as you lustfully stare at her across the table.
And then she gives herself to him
For the price of a meal? That ain't no "lady"!
Our dating behavior is based on this sexual play that goes back in our culture for centuries.
Aspects of it are, but these vestiges of previous times are no longer operative in our culture. Usually it's just going through the motions because it's easier to conform to social norms, whatever their source.
Anyway, all this is far removed from the OP's original question, which was whether being expected to "go Dutch" is an acceptable reason for not dating someone. It has nothing to do with post-dinner expectations.