A billion times this. School is not to train you on Math, English or Science. It's also to teach you how to cooperate, how to reach consensus, how to make decisions as a group, and so on.
These soft skills are absolutely critical to maintain a properly functioning society.
Now, such organizations are banned. The closest analogue is a "student" council, run by an adult, that might get to choose the color of the wallpaper at prom.
Cooperation requires shared goals. I can't cooperate with someone when we're not sharing goals. Young students don't have shared goals other than "survive in this classroom for 11 months out of a calendar year". So there's no lessons in cooperation.
>how to reach consensus,
Of what use is consensus, without shared goals? Sounds more like indoctrination.
>how to make decisions as a group,
Same as above.
>These soft skills are absolutely critical to maintain a properly functioning society.
These skills are actually being used to murder civilization/society, even as we speak. The current fertility rate is sub-replacement, but the children being indoctrinated in public schools are being indoctrinated to be even less fertile than that. Many will grow up to be and remain childless as adults, and as that happens, society will not replace those people who are dying of old age. Society then dies itself just decades later. Your society, such as it is, is absurdly dysfunctional. I suppose if one were to define "properly functioning" as "polite to a fault" or "as peaceful as cattle trudging down the slaughterhouse chute"...
Sure, there is selection bias among those who get that far in math, and those who would seek out tutoring. But I had 9th graders coming to me already behaving well as adults. More often than not they were in charge of working things out with me, not their parents.
Every time one of these threads comes up I cringe, because virtually nobody here has worked with a large number of these kids. They just remember the one weird kid who stood out. If homeschoolers were to put forth the same arguments based on the one weird kid from public school, homeschooling would win by a landslide.
People say it's about socialization, but homeschoolers are out there doing it in a normal way all the time. Parent needs to go to the post office -- there is a class on that, and why. Everything can turn into a lesson and not just something taken care of by parents. They come out of this experience with far more adult level socialization and civic knowledge than the average kid, by a wide margin.
Who are kids in high school getting their social queues from? The drug dealers? The bully? The good kids in high school are typically well adjusted because of things taught to them not by their peers, but by their family and community outside of school.
Yes, homeschooling can be done poorly. But it is not inherently a poor education, and in my experience is far superior to the average experience at a public school. Some exceptions apply for those things which a large school may be able to have by aggregating sufficient students and resources toward (marching band, science classes, AP level courses).