Men opening doors for women, for no other reason than chivalry, is a small thing in the grand scheme of sexism, but it's an example of a patriarchal sweetener. It helps to hide the oppression of women as a group by men as a group.
I'm not saying that individual men consciously think "here's a chance to oppress women for the good of the brotherhood". The man's actions have been conditioned by society since childhood. He has been taught and encouraged to open doors for women, and patriarchy benefits indirectly from this. It was probably his mother who taught him and she won't consciously have been thinking "let's oppress women". It has just been treated as the polite, accepted, expected, normal, traditional (but patriarchal) thing to teach young boys.
Men own most of the world's property, so when a woman is granted the so-called "female privilege" of having a door opened for her, please remember that the door is in a building that is probably owned by a man.
Door-opening has been a small patriarchal habit, which has deflected most women from asking, "would I rather have a man open a door for me, that I'm capable of opening myself, or would I prefer joint-ownership of the entire building?"
Likewise, men paying of restaurant meals. It has deflected most women from asking, "would I rather have a man buy me dinner (often with his expectation of sex in return), or would I prefer to be paid as much as him for doing the same job?"