When your boyfriend says he's old fashioned?

Like a woman HAS to cook and clean. A man has to protect and provide. I had an argument with him about this last night. I said a woman doesn't HAVE to do anything if she doesn't want to. He's was saying that a woman, when in a relationship has to take care of the other with cleaning, cooking and other. Like if he's unable to clean up after himself, she has to do it. And if she only cleans up after herself she's only considered a friend. And if she was a good girlfriend, she would clean up after him. After he eats, makes a mess or whatever. And I'm like wow, no. She cleans when and what she wants, she's not obligated to do anything after you, she doesn't need to walk around behind you and clean up every mess that you make. He's like, I hate feminists. I said yeah, if you're married, it's a partnership.  One person is not supposed to do all of those things. Both people have to contribute, not just the woman. And he says again, it's what a woman does! Just as what a man does! I'm not going to mix the two because that's just wrong. What do I say to all this?!