Children are not empty vessels that you pour knowledge into. They are individuals with unique interests and aptitudes. There is no universal formula for what to teach, and if a kid has no interest or aptitude for a subject then there is almost nothing you can or should do about that. Let them develop how they will, and offer them assistance on things that they like. Expose them to things that would complement their unique personality.

There were two popular submissions 3 months ago:

Teach your kids poker, not chess: https://news.ycombinator.com/item?id=31435034

Teach your kids bridge, not poker: https://news.ycombinator.com/item?id=31459044

Ability to work and play alongside other people, even people not exactly like themselves.

Good numeracy and literacy. In particular not being fightened of STEM subjects.

I'm a school governor to help make education better for my kids and those around them. Many of my relatives went to (very well known / pricy) private ("public") schools and I wouldn't consider anything other than a local normal school for my kids, now in their teens and doing well. It's worth noting Plomin's views[1] on what overdoing education actually achieves...

[1] https://www.goodreads.com/book/show/39074555-blueprint

The concept of non-negotiable or required skills seems wrong. I unschooled my three children, which meant letting them choose what to study and when. They all learned to read early on and managed to get enough education to function in the world, including going to college if they chose to do that. Children naturally exhibit lots of curiosity, you probably don’t need to force subjects on them.

Homeschooling with a rigid curriculum, something I associate with religious homeschoolers and parents trying to protect their children from the “real world” while simulating the classroom at home, seems like the wrong approach to me.

How to get along with other people. Reading and math. How to take things apart. How to know where home is.

Mostly it's a matter of NOT crushing their curiosity, and engaging it positively whenever it shows up.

Latin. It opens up a world of historical knowledge through fascinating first-hand sources that are otherwise inaccessible. I wish I were better at it.

Just sales. Transferrable skill to whatever interest they want. Also teeaches them self reliance and responsibility.

I might also teach them how to google.

I try to dig into my children's interests.

Sometimes it is outdoors survival stuff, model rocketry, playing with instruments(they never want to actually take any actual lesson), and electronics.

I want to have them see me work on my own projects and read and be good in the world too.

Curiosity, sales, survival (including emotional fortitude and establishing boundaries). Everything else can be acquired on their own.