Equality: Of course I can open the door for myself!
Chivalry: I am not challenging your ability.
New Chivalry: I'm asking you to hold the door for me, please.

Equality: Of course I drink and smoke!
Chivalry: I'm not challenging your decisions. 
New Chivalry: I'm asking if I can bum a smoke from you, please. 

Equality: Of course I can pay for our date!
Chivalry: I am not challenging your capability. 
New Chivalry: I just wanted to ask if you can pay for the movies too, as I'm broke.

Equality: Of course I can go home alone!
Chivalry: I'm not challenging your independence. 
New Chivalry: I'm just asking if you can drop me home on the way,...