illini, I don’t have it in front of me now, so don’t act upon it yet without first consulting your local Orthodox Rabbi, but I am fairly certain that we pasken that if there is a man and a woman on a sinking boat and only one could be saved, you save the man first. (The opposite of the “chivalry” demonstrated on the sinking Titanic.)
I think the reason mentioned is because of the responsibility’s incumbent upon a man. (Same as why the brocho sheloi usani isho is made.)