hhmmm. chivalry.... interesting word with mediaeval and romantic connotations. I'm not sure about chivalry but I am sure about courtesy, manners and politeness and yes, I DO expect those from men. I also expect courtesy, manners and politeness from women and both genders will receive the same from me.
If I go through a door, I will always look behind to see if anybody is following and hold the door open. I expect that of anybody in return.
If I am approaching a door at the same time as someone else, I will open it and let them through first.
If a man does the same for me, I will thank him and assume that he has done it because he was well-brought and well-mannered, not just because I'm a woman.
It must be so difficult for you blokes to remember when you must be polite and when you needn't be - try doing it all the time and then you can't complain of unequal treatment or expectations.
Cheers
Whirls