I’m sure these motivations do play out in some circles. However, every single homeschooler I know personally, and I know quite a few, does so because they want their children to have a very specific kind of religious education. Often the way this plays out is that they homeschool for a while, transition to a denominational school, and then depending on the family they may stay there or make a second transition to public school around 9th grade.
I think this tendency is heavily dependent on where you live. We have great public schools that will track advanced children aggressively if the parents push for it, so the motivations you list are unusual in my area.
Religion is definitely a big motivator. My perception though is other motivations have been on the increase, especially since the pandemic. One other group attracted to homeschooling is the hippie-type who thinks school is some kind of diabolical machine designed to crush kids' souls. Since the pandemic there's also been a big surge in the "I don't trust vaccines" group (which already had a good deal of overlap with the hippie group).
I have a feeling a really large percentage of homeschooling is about religious separatism and political separatism, and not about academic performance. Yes, you'll hear HN commenters sing the praises of homeschooling because this site is going to be disproportionately represented by the group doing it for actual educational reasons.
Also, we HN commenters typically see the success stories around us at work, not the failure stories. We all know that guy on the QA team who's a genius and credits his success to homeschooling, but we don't know the countless numbers of grown adults who are trapped as housewives who can't get a job because they never learned 5th grade multiplication.
Both were certainly major motivating factors for my parents’ choice to homeschool me in the 90s. Quality of education was a concern too, but it very much took a back seat to the other two.
The overwhelming majority of other homeschooling parents they had contact with also held separatist motivations.
That may be so, especially if you add a sort of "cultural separatism" (a la the hippies I mentioned). An odd thing I see recently too is people who seem to believe they're making various choices for educational reasons, but it's not clear if the education they're moving to is any better. They just do it because they perceive their child as being unhappy or stifled somehow. There seem to be, for instance, more and more parents who believe their kid is unusually smart and should be on some kind of fast track or not have to do certain things, even when there's little objective evidence of the kid's abilities.
Vague "educational reasons" is always the noble-sounding excuse they use, but often if you dig deeper they'll admit it's more about the various forms of separatism.
Sometimes you don't have to dig. A ton of moms in my wife's church group permanently pulled their kids out of public school in recent years, and they will openly admit that it's about keeping their kids away from "those" people, where the definition of "those" runs the gamut.
I don't want the separatism, but I also want the ability to give my kids a decent education. There ought to be some way to determine which is which. Do you have any ideas?
We did the homeschool thing for one year after most kids went back to school after COVID. My wife has underlying medical conditions that made her quite concerned about catching it before the vaccine rollout. We did a few of the homeschool group organized field trips and I got to briefly meet some of the parents. Overall I can't say much about the kids, they seemed fine. The parents were friendly, but when I asked about the curriculum they almost invariably suggested PragerU material, which makes me concerned for their children's future.
I think this tendency is heavily dependent on where you live. We have great public schools that will track advanced children aggressively if the parents push for it, so the motivations you list are unusual in my area.