The way I look at is as, we are all good at different things, its the harmony of the relationship that counts. I personaly have lived alone all over the world, so I had to learn to cook, wash, iron, houseclean and all the other things that go with having a house. I never tell my partner what to do or what not to do, if I have to do that then I picked the wrong partner.
What you do, you should do together and share the fun together, I love to cook together, Its fun and interesting. Equality is difficult because we all have different abilities, so equality in individual aspects is not easy but taking what the individual abilities bring to aa whole to partnership, there we should be equal and respected for what we bring to the partnership.