There’s no need to make such a sexist statement. I have cleaned my own clothes since I was a child. My wife had never done the laundry until she moved in with me.
I didn't read it as sexist in itself. It wasn't advocating for a female bias in laundry work, it was highlighting that the female bias does still exist in some households.
I can contribute, like you have, that in my household the balance is different. This doesn't refute the observation, though.