I was "home educated" - the typically British middle ground. Not "home school" (school at home) and not unschooling. But self-educated / family educated at home, for the whole of highschool level. We'd just moved country, and didn't want to jump into a new school system straight away. It worked pretty well for us. I spent a lot of time learning to program and play music, I joined a local drama group, played in the church band, the town marching band, and taught myself to juggle. My brother did loads of piano, singing, and IT stuff. He's now working as the IT and music teacher at a local private school (after having gone on to do his BA and MA in Theology, as well as a teacher-training certificate), and I'm working as in a non-profit doing all kinds of things. We decided, my brother, my parents, and I, to use a curriculum for a few years, which allowed us to get International Baccalaureate equivalents, which was useful for my brother with going on to Uni, but useless to me. We learned a lot of useful stuff though.
I learned all the sine / cosine stuff around age 10, as I was trying to write a computer game and needed to move things around circles, so asked my mum about it, who asked her friends on the home-educating-parents email list, and eventually someone helped. (This being in the late 90s). I wanted to learn it, so I did. I can still remember everything I need to know about those because it was interesting to me at the time. I never learned to spell at school. I was awful, always in the lowest group in class. Until I wasn't doing spelling tests, and just writing on my own at home on the computer, and kept getting annoyed at the little red squiggle under half my words. My brain eventually learned it was quicker and less distracting to my writing to learn the correct spellings rather than having to go back and correct them.
I do think a certain amount of "education" is required for a sensible life. Reading, writing, arithmetic, geography, etc. But once you've learned to read, and if you've had a love of books instilled into you, you'll probably pick up most stuff you really want to learn along the way. And there's no real reason to force any of those skills at any particular age. My brother learned to read at about 3 and a half, as I was learning in kindergarten, he decided to too. I have another friend who simply wasn't interested, and didn't learn until about 8 and a half. But then he learned to read and write in about 2 months flat.
Kids are all different. Public education was a brilliant, wonderful institution to help move millions of families out of poverty and enforced unskilled labour. But once you've moved a society out of that state, education needs to be much less of a "life support" type system, and become more of a individualised therapy / explorative / personal journey.