To me, doing housework is not just work or duty. It is responsibility, not something money can buy.
I might not clean, wash or mop as clean as a professional cleaner; I might not cook as good as a chef out there, but I am proud to do that for my family.
Unlike professional cleaner or maid who does the job for money, when I do housework I make sure I put my heart in, because I care and I value the works contributing directly to my family. I want the house feel hygiene, tidy, clean and comfortable , i want the food to be yummy yet healthy, etc.
At home, XH and I almost practise 'meritocracy' and preference... there is no fixed women's or men's jobs at home, we just figure out what is best each can do. So, the 'division of labour' goes according to ability and preference but not along the gender line. No paksa, only rela.
I cook, because XH thinks that I cook better (and I also enjoy cooking). She sews, because I am really chor lor and lunzhun, can't handle tiny things (and she thinks she is better too). We clean using different methods at different time. We wash dishes depending on who is more free at that particular time.
House belongs to the members who live in. Everyone has responsibility to take care of one's home. I was 'trained' to do housework when I was young. I learned to be independent when I was abroad. Do housework is just essential life skills, both genders should learn, no excuse. For sure, I would train my kids to do housework when they grow up.
I also find that, when doing housework yourself, you train yourself to be humble. You would appreciate but not look down on cleaners who also sweat for doing their job for the communities.
The way I see is, housework should not be difficult things to do, both men and women should be capable of doing the same set of housework. So, gender equality should start from home. Do not let anyone tell you that you should (or should not) do certain housework just because you are woman (or man). Tradition can be changed. Respect housework duties and responsibilities.