Is there inequality in life and death situations?

My partner believes that if women truly want equality that they can't pick and choose what situations they want to be equal in. He said women would find it unfair if they were expected to investigate noises in the middle of the night the way their husbands are, or fight off intruders to protect their families (in the instance they are living with a man) or if they had to give up their seat to a man on a life boat on a sinking ship. So my question is: Do you think that a womans life is considered more valuable than a man's? Is this an outdated notion or is there some reasoning behind it?