You could explain how patriarchy assigns the important roles to men and the less important roles to women as a means of subordinating the female sex,...
But why do you say that caring for the home, keeping the home functioning and regulated, is less important that, say, going to some office to do help keep someone else's company running?
I'm not a fan of housework. But I also didn't like the work I did when I was an employee. When I had children, I decided what I wanted was to stay home and do the domestic work because I would rather clean 100 floors than dictate 100 more letters about matters that basically didn't interest me. I chose the domestic work and I was glad that, having given birth to my children and breastfeeding them, I was already closer to home in order to do it.
We had a clear split of duties. My husband did ALL of the finances, taxes, paperwork etc because I loathed that. I did most of the DIY at home. He did all of the gardening, as he had green thumbs and I didn't. I did all of the childcare, because I enjoyed that. I cooked, he washed up.
I think we should stop thinking like men, which is exactly what that first sentence does, by designating certain jobs to more and less important.
Domestic work IS important, very much so. Raising children well IS important.
Men in office jobs today like to tut tut about women's dereliction of duty, but they've shirked nearly every scutwork responsibility imaginable. Many of them moan and cry if you so much as ask them to take out the trash.
This, however, is very true. I much prefer the old-fashioned kind of man (like my late dh) who pottered around in the garage and cleaned the gutters and chopped trees for the wood-burning stove and taught the kids how to split wood. It was a clear division of duties and we each respected what the other did, and didn't want to swap.