See my other reply [0] for more. I think the word homeschooling groups together to many different things. Something like "distributed schooling" feels better for my experience, and the people in my community.
Personally, my mother was good at writing, so she taught that subject until I was 12. After that, there was a local writing teacher who taught an equivalent of comp 1, and comp 2.
My father taught math and programming. We did a mix of typical tutoring, and self study. Lots of self study since I had a natural aptitude for it.
From my experience, the horror stories you hear about kids being stuck in the middle of nowhere with only a bible to read are not the norm, and not what most "homeschoolers" advocate for. Even the word homeschool is a misnomer, a large amount of my time was spent at a local co-op with other "homeschoolers". My wifes youngest brother spends 4 out of 5 days split across two local co-ops. Her eldest brother is in a PhD program after the same experience. Most of the homeschoolers I know are more than able to function in modern society. Homeschooling simply allows for a much more tailored and less systematized schooling experience, making each family educational experience more akin to a startup in its ability to be nimble and respond to individual needs.
Good. The current state of the world is incredibly unnatural when you compare it to even 50 years ago. Everything is too connected. We are so much more efficient, but so much more fragile. The best thing you can do to save the world is save yourself and your family. Less fragility, more robustness at the personal / local level.
I am mid twenties, and was homeschooled my entire childhood. My father owned a technology company, and brought me to work with him most days. People talk about homeschooling being damaging due to the lack of exposure to the "real world", but I have had more exposure to reality than most, due to the constant exposure to actual working life.
Don't be afraid of "sheltering" your children by not having them be part of the system. There is so much more out there than the system. Your kids will turn out weird vs other kids raised in the standard environment, but its a good kind of weird.
My family was very involved with the homeschooling movement in our state, so I am more exposed than most to the sub-culture. Feel free to ask me any more specific questions.
[0] https://news.ycombinator.com/item?id=23874714