There are MANY reasons why the goyish practice of chivalry is incorrect. When you open a door for a woman to go in first (as is practiced in a chivalrous society) you are walking in behind her. Not tzniusdik. And like someone pointed out previously, when it comes to saving lives halachicly we are obligated to save mens lives first, if its an either/or situation (unlike how it would be done in a chivalrous society.)
