Second: There are communities (homeschool co-ops and such) that can help.
Third, though: Do not underestimate yourself. You know a lot of physics for a third-grader. You can teach that, even if you have to read the textbook right beside the student. (You may not be able to by high school, though.) And you have a great advantage. One of the key things in teaching is classroom size. The difference between a classroom of 30 and an classroom of 4 is massive.
The help I need is provided by the public education system. The help is in sending my kids to public school.
pffft. Put two skittles next to three skittles and ask what the resulting summation is in terms of skittles.
I'm being a bit glib, but the reality seems to be that many smart people think teaching is trivial, a simple case of knowledge transfer. If you understand it, surely you can teach it to someone else.
My personal experience at uni suggests that truly brilliant people who understand topics perfectly can be Not Good at instilling understanding in others. It's a different skill imo.
Is it the solution? I dunno, but public schools are getting worse by the year so I understand people trying something different.
Teaching one or two students whose home situation supports you 100% is a much much less daunting proposition than trying to teach a class of 30 kids (or several such classes).
The idea that teaching things to your own children (which all humans have done forever) requires specialized training and credentials seems silly. But again, that's a very different job than being a school teacher, I think.
If you were taught anything extra, it was from a private school or tutor -- the majority of humanity is clothed in ignorance.
Children were taught what they needed to survive, e.g. farming, fishing, etc.
My spouse homeschooled our daughter during the first school year of Covid, and it was challenging. You are completely reliant upon the materials you source, and there's no definitive curriculums.
Personally, I cannot realistically conceive of many people actually teaching their kids any science, literature, or critical thinking skills.
https://www.eurekalert.org/news-releases/522078
Home schooling can have an academic advantage where parents are intelligent, well educated, above average in patience, and value education for their own kids.
IME it's more likely one of the home schooling parents had some bad experience(s) in traditional schools and are overreacting.
https://health.ucdavis.edu/children/patient-education/Positi...
https://www.rasmussen.edu/degrees/education/blog/parental-in...
Your stats aren't all that meaningful for the following reasons. What percent of homeschooled kids meet the criteria for "structured homeschooling"? Without this information it's not a meaningful stat.
There is also selection bias going on. They tested reading, writing, arithmetic. Did they test algebra? Did they test biology? I'll bet a fair number would fail at questions regarding evolution or have a skewed view of historical facts.
My guess is Dunning-Kruger effect and studies highlighting academic benefits from homeschooling.
The general reason parents can confidently provide primary education is that a) good educational materials are easy to research and acquire, b) the benefit of education closely tailored to a child's strengths and weaknesses meets or exceeds the benefit of institutional pedagogical theory and classroom management skills.
In secondary education years, access to material and closely meeting needs still factors, but the parents' operating principle is increasingly about pulling in the best sources available. That often means community college or part-time high school classes.
There are also a lot of homeschool co-ops, pods, and other resource and skill-sharing arrangements. Lots of variety.
All your examples of authority figures are trained to be effective over a high volume of lower trust interactions with the general population, relying on professional incentives to perform. They are needed but they're most effective when complementing and backing up parents who cannot for whatever reason provide care, correction and education at home.
What makes parents with no specialized training think they can do better than the public school system?
My sister homeschooled all 8 of her kids from kindergarten through high school and it shows. It especially shows among the younger kids. Three of the younger kids clearly needed special help and had learning disabilities but her pride prevented her from getting them tested or even acknowledging the possibility that she was wholly incapable of adequately teaching them.
What is it about teaching that makes people with no training think they can do better than trained professionals? Do such people think they can be a police officer without training? a nurse or doctor without training?
I don't intend this to be confrontational. I'm curious about the thought process. I know there are cases where a parent can be better than what is provided by the public school system but I think far more parents are homeschooling who shouldn't be. I assume you are the exception and your efforts at homeschooling are justified.