"She said" is a very revealing part of that statement, for therein lies the fallacy that there is any unfairness.
My experince has been that, in fact, the women do a disproportionate amount of the work around a household, but a moot point has always been that they also "invent" a much more disproportionate percentage of the " must do list": a self-fulfilling prophecy.
"Are necessary" and "I decided it must be done" are two entirely different things.
e.g. "I decided to install chintzy dust-collecting ugly curtains on every opening in the house, including the chimney!"
Attitude amounts to so much. Many women I meet have a tewrrible attitude about men, that we are hear to cater to every whim, every complaint, evey nuerotic belief, and should get nothing in return.