You might think it makes sense for one person in the family to specialize and to do all the housework. However, there are many possible benefits to be obtained from sharing housework equitably:
1) All people involved appreciate housework more, since they have personal experience with it.
If you don't do housework, you can forget how much effort is involved in planning meals, sorting socks, or vacuuming, and you might not appreciate these tasks enough when your spouse or parent does them.
If you are involved in housework, you are frequently reminded that housework matters--and it's real work.
2) Avoids resentment from housework not being appreciated.
By principle (1), knowing what's involved in housework helps people not to take others' housework for granted. If you cook dinner a few nights you a week, you have a better idea of what went into a dinner that someone else cooks for you.
3) No one's time seems more important than others'.
Putting housework onto one or a few people implies that their time is less valuable. In contrast, sharing housework says loud and clear, "We are all equal here. We all have important things to do besides housework, which is why we share it equitably: to limit the load on any one person."
4) Instills gender equality in the next generation.
You can say what you want about gender equality, but there is no teacher like example. Share housework equitably, and children will grow up thinking it's normal to do so, not to mention perhaps picking up some messages about gender equality along the way.
5) Makes it more fun.
Sharing housework can make the difference between it being an onerous burden for one person versus a pleasant diversion for several people.
Doing all the housework for the entire house is a huge burden. But cleaning the bathroom once a week could be a fun tradition; and making dinner every other night or once a week could be an opportunity to be creative.
If the magnitude of housework is not too great, one is more free to enjoy some of its enjoyable aspects, such as clean-smelling sheets, clothes warmed by the dryer, fresh smells of natural cleaning solutions, cooking, and the pride of having created a meal.
6) Lightens the load.
Doing a chore half as often can make it even less than half as burdensome, since you get a break in-between times when you have to do it.
Similarly, running a long run every other day is less difficult than running that same run every day. It's all about getting emotional or physical breaks.
7) Fewer things for each person to worry about.
On days when someone else is cooking, you don't have to think about what to make for dinner. If someone else is responsible for cleaning the shower, you don't have to keep "shower cleanliness status" in the back of your mind.
8) Reduces the total "housework burden."
All in all, if people are good about doing their parts, the burden of the housework on the individual people should sum to less than the total housework burden were it to be borne by one person alone.
Having it all on one's own shoulders can add an additional element of fatigue beyond the work itself. Others sharing the work eliminates the feeling of being responsible for everything.