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"...
They risk being able to function better in highly controlled environments with other kids that share the same background as them. Not optimal.
You're right on pointing out the environments in which homeschoolers often perform poorly, but you used the wrong word. Homeschoolers are bad at more controlled environments, where you must work within the confines of bureaucratic systems run by people who didn't design them. Timesheets, changing place when the bell rings, studying only what's on the test and reproducing at the correct time, speaking differently to people based on how much authority they hold over you according to a system of record--that is difficult for people who are used to a lot of freedom in terms of how they spend their time, and how they interact with other people.
to be clear, i do believe that tough personalities that aren't straight up bullying can still happen inside of a group homeschooled environment.
I think the way to handle socializing kids if you homeschool is to enroll them in extracurricular activities where they can meet all kinds of people. If the activity is a good one, you'll still probably avoid the worst types that appear in public schools, and give the kids more exposure to different kinds of people. And if it doesn't work for some reason, you can switch activities or groups more easily than you could ever switch schools.
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).