There is a single opinion that is valid of all those different forms together: it (home schooling) will increase inequality in society in terms of amplitude, spread and flavors.
I'll answer here for everyone. Some projected connotations on my comment, others were more neutral.
My comment was actually intentionally devoid of connotations and just exposed a direct consequence of the nature of home schooling compared to public schooling. Home schooling simply has many more input variables (wealth of parents, religion of parents, politics of parents, etc. ) and therefore the outputs are much more spread out. Home schooling is an even more individualized form of private schooling and on an axis of equality, an "universal free public schooling only" system would be at one end of the spectrum and a "self funded home schooling only" system would be at the other end of the spectrum with many options in-between. My statement that home schooling is more unequal should not by itself be controversial. If follows directly from what the thread ancestor said, to quote: "People talk about homeschooling as if it's one single concept, but it's actually a whole bunch of very dissimilar things."
What is controversial is whether equality or lack thereof is desirable.
I will argue that striving towards more equality results in better social outcomes.
Before that, I will note that just as parent said above, it is perfectly normal for any parent to desire the best for their own child.
1. My fist argument is that, as parent said, most people overestimate their own capabilities and the quality of their own decision making. All of the different categories of home schooling parents desire the best for their kids and imagine that they will have above average results yet very few will actually be above average, many will be below. I would argue that in this case we are talking specifically about equality of opportunities, and that while a few home schooled students will gain extra opportunities, most home schooled students will be robbed of opportunities that a public education would offer. AS a most extreme example, a flat earther insisting to home school their children and only present "alternative truth" is a danger to their children.
2. My second argument is that a more equal educational system is likely to result in a better adult environment for a student after they finish formal education. In other words, for better outcomes for ones own student it is worth spending on the education of other students too. This is because:
2.1 With more uniform educational outcomes a person will be part of a larger cohort and demographically it is more advantageous to be part of a larger cohort. The group of like minded people being larger means there are more social opportunities which result in more opportunities for both dating and professional networking.
2.2. Even presupposing a home schooled student is a winner and has way above average outcomes, it is better for them to live in a society with a higher baseline of education. Going by Carlo Cipolla's "The Basic Laws of Human Stupidity", which splits people into 4 groups (intelligent, helpless, bandits, stupid) based on 2 criteria (benefits/losses that individuals cause to themselves and benefits/losses that individuals cause to others). Cipolla's 5'th rule says "A stupid person is the most dangerous type of person." And the corollary is: "a stupid person is more dangerous than a bandit". Therefore it is advantageous to the intelligent people to minimize the share of stupid people. A higher baseline of education is a way to hopefully achieve that. The only group that believes it is advantageous (at least on the short term but not on the long term) for the share of stupid people to be larger is the bandits.
3. My third argument is that, educational competitive pressure is detrimental to the health (especially mental and emotional, but also physical) of students. A more unequal educational system results in more competitive pressure. As can be seen in China and South Corea, extreme competitive pressure will result in peaks of performance but will also be largely detrimental to the well-being of the students during and after the years of formal education.
