The Oxford English Dictionary’s first definition of chivalry is:
The medieval knightly system with its religious, moral, and social code.
It is based on Christian moral values.
Why shouldn’t the girl open the door for her date? Because the Christians do it the other way so you’re going to now call it a “common courtesy” based on how the goyim live? There is no logical reason why the girl should not open the door for her date rather than vice versa other than to follow the common goyish way.
If you can think of another good reason why she shouldn’t open the door for him, please let me know.