First, don't limit your child's education to what you are good at. That is doing them a massive disservice. You don't have to be good at teaching something for your child to learn it. You just need to find and provide resources and help them self-navigate the topic.
Secondly, who cares if AI can do something better? That doesn't mean to avoid learning. People play chess even though grandmasters exist who will always be better than them. People learn to write even though there are professional novelists and poets. Not only is it OK to learn something even if others are better at it, that is kind of the entire point of education.
Humanities is also worth it, if only because it makes life so much more interesting. However it's not one of those things that can be forced upon someone. I hated a lot of it until I got to enjoy it on my own, without pressure.
I am not a parent, and I have no skin in this game, but I think that the future will still have space for a well-rounded human being. Even with all the fancy new tech, your child will still need to fix flat tires, negotiate, navigate ethical conflicts, cook, communicate with other people, apologise, speak up, and all the other things.
It's better to learn commutativity with "integer" than with "simple groups". You hand needs to know how to do the operation to get intuition to understand what the computer is showing in the screen.
You can probably drop long division, like we dropped long square root a long time ago. They are nice algorithms, so it's nice to revisit them if he is interested when he is a grow up. (Even logarithm tables and slider rules are interesting, but not for everyday use.)
Long sum and long multiplication are too important, don't drop them, probably only for 3x3 digits. Left the 17x16 digits cse for the computer.
Approximation is super important but super hard. I've seen a few attempt to teach that to 7 y.o. kids, but I think in most cases small kids should learn exact calculation that are easier.
On the other hand, as was noted before the AI rush and before the recent political turmoil (but they will only have exacerbated it), the value of capital increasingly outweighs the value of labour. So if you want to have grandkids you might want to make money using your own skills while it's still possible.
You haven't said why you are home-schooling?
The biggest educational determinator of life outcomes is literacy and the biggest determinator of career outcomes not already set at birth is social fluency.
Some suggested reading for the OP that other commenters haven't already touched on:
Tears (2014) - by Kevin Simler, ex-product manager for Palantir Technologies, Inc.: https://meltingasphalt.com/tears/
How Stanford teaches AI-powered creativity (2025) - by Jeremy Utley, director of executive education at the Hasso Plattner school of design: https://youtu.be/wv779vmyPVY
A Billion Voices: China's Search for a Common Language (2016) - by David Moser, former Dean of the Yancheng school at Peking University: https://archive.org/details/billionvoiceschi0000mose
Pre-ASI: The case for an enlightened mind, capital and AI literacy in maximising the good life (2025) - by Hock (pseudonym): https://alitheiablog.substack.com/p/pre-asi-the-case-for-an-...
The Resourceful Life (2023) - by Venkatesh Rao, ex-Xerox consultant and author: https://www.ribbonfarm.com/2023/07/06/the-resourceful-life/
Prep for the worst, hope for the best. So, if the AGI, UBI doesn't happen, that still would be ok. And if it does, knowing things that are useful, how those AGI things work might come in handy. Maybe those will end up empowering the kids.
The uproar you see on HN is because most developers are web front-end or back-end developers and LLMs do especially well at those tasks because they have a lot of training data to work with and also because there are also a lot of influencers, snake-oil peddlers, and doomsayers trying to hype AI up for their own gain.
It also takes foundational knowledge to know what to type into a calculator or LLM.
I think the ^ are the minimum a good citizen needs. If you can't teach all of them maybe let him go to school as well, or hire someone to do the part you can't.
Regarding the future, yeah I share the some worry, but I guess we all have to go through it.
Math has been a staple for hundreds of years.
Being flexible and working in industry's as they start or change will help.
Psychology - Mind _is_ Everything. Psychology is just applied philosophy and teaches one to understand/modulate our mind according to a worldview.
Logic/Maths/Science/Engineering/Technology - To understand the objective world and earn a livelihood.
Humanities/Art - What makes us Human. May/May-not earn a livelihood.
Worldly Wisdom - How to adjust to people/society to get what you want.
AI/Programming/etc. - Tools to be used in aid of the above but not an end in themselves.