Both of my children were Home Schooled until High School (technically 7th and 9th grade). They've been students at a private school and now one attends an excellent private High School and one attends the 4th best High School in my state.
They are straight-A students (lowest grade: 94%; History -- my Daughter). They are shocked that they attend school for 7 hours a day and there are kids who "struggle" while they finish their homework on the ride home, don't study, and get the grades they get. They are in advanced classes and both have had a perfect score in Math all three years. Mom and I are also divorced and have been since they were 2 and 4. They make friends easily but struggled when they were Home Schooled because they have less exposure to kids their age. They were given the choice when my son hit 9th grade "continue or attend Public School or a school we can afford). They didn't want to miss out on "The High School Experience" but both, enthusiastically, want to Home School their own kids one day.
They aren't unique/gifted. There are plenty of students at their schools who do as well as they do and were not Home Schooled. The difference, though, is they "did school" in a given weekday for never longer than 1.5 hours. Most days were 30 minutes. September-April with summers off and that was it.
Religion was not a factor in our choice. My son's ASD Type 1 diagnosis played a role, the way Math was taught to me played a role, the arrogant belief that I could do better and the fact that my ex-wife didn't work played a role. Mostly, talking to other Home Schooling parents and their children and "wanting my kids to be like that" was the primary factor. Watching a 13-year-old speak intelligently and with confidence about a subject they understand and actually expect an adult to listen to them is kind of crazy, especially when they really are intelligent and should be listened to.
In a decade of Home Schooling, I have talked at length with hundreds of families and their children who took that path (various conferences, Home School events at local businesses, and extra-curricular activities done "during the school day" for Home School kids). I've observed a few things: All of them teach as much as we did. None of them will admit to it until their kids are in college or they decide to send them to traditional schools and "their child's education is validated by someone else." Nobody who is actively Home Schooling will admit to an outsider that their children get 1-1.5 hours of education a week day because you'll call CPS on us. All of their children are about a year or two ahead of children "their grade" despite this minimal amount of lesson time.
I read over and over and over again about how Home Schooled children are ignorant, don't believe in evolution, believe the world is flat, their parents don't actually "teach them" -- I have no doubt those children exist and I haven't seen them because the Home Schooled families I encounter attend conferences, belong to groups (we didn't), and care about their child's education. I live in a state that, at one point, had the largest number of practicing Home School families (not sure where it is, today) and the most liberal rules around it -- literally "take them out of school"; that's it.
Everybody seems "to know some invented Home Schooled child" who had some kind of major life problem. I usually challenge for specifics and it's always turned out the kid doesn't exist. Knowing any child who is Home Schooled is unusual. But knowing the one child validates your choice to NOT Home School, the statistics of which make them extremely rare, and you find they're parroting some anecdote they heard. My daughter's school[0] has about 1,700 students in it. Her last had about 500. I have asked every single one of her teachers, her counselors and several teachers they don't have "have you ever had a Home Schooled kid in your class, before?" I'd guess 40 educators and some staff/administrators. There's exactly one who had exactly one child in her class at her last job who was Home Schooled. He was an excellent student. And this in a state that has a lot of Home Schooled students. Judging by Facebook, you'd think there's one hiding around every corner peeing in people's Cheerios.
I suspect it's people feeling (needlessly) insecure about the choices they made for their own child and feeling threatened by the fact that I chose differently. I don't encourage people to choose to Home School. It's not for everyone -- for starters, you can't do it with two full-time working parents and that means it's simply not an option for most people. However, this topic very rarely came up without judgement from everyone who didn't Home School about what a dangerous choice I made when I was still Home Schooling. It's a lot more fun, now, since I can point to their success.
Yes, some Home Schooled kids struggle/drop out of college or can't hold down a job. Certainly none of us have met a kid who drank his way through Freshman year of College, or was ill-prepared by their public school and failed out. And we came from High Schools where everyone received a degree, too. Studies continually affirm the success of Home Schooled students, yet "everyone knows some Flat Earther child from Home Schooled parents." Children fail in every type of education. They fail less in Private schools and Home Schools. They fail more in Public school (largely because of "everyone goes there, including children in extremely difficult life circumstances"). The problem is that these wrong impressions of Home Schooled kids turn into laws that ban or curtail the freedom to have the choice of Home Education.
I know if I had chosen a more traditional route, my kids would have had the same probability of success. I would have been deeply involved in their education whether or not I was the one teaching them and that's how you get successful students in traditional education, too. While it might be nice to stand on some high horse, claim that "I just love my children more than you did", pretend that all of this was some massive sacrifice and I'm some super-parent by comparison to all of you who went the traditional route, that would be a self-aggrandizing lie. I paid for and followed curriculum. It was easy. The only challenging part of it is that "your kids will argue, yell and cry at you when they struggle"; they won't do that with a stranger.
With all of the extra non-lesson time they had, it was probably easier for them to excel. But I don't look down on people for not making that choice. Quite the opposite, everyone looked down on me for the entire duration that I was a Home Schooling Dad. It's silly.
And I'd do it all over again if given the choice for one reason alone: My kids are incredible self-learners and that was the one thing that I was very intentional about. Both of them have the confidence that "nothing is beyond their ability to learn" and that it's a simple matter of finding the right information, studying and practicing. My daughter is a shining example of this: She has learned to plays Guitar, Drums, Bass, and Piano (some proficiently, some she's well on her way). She has never had a lesson. She can read music and tabs and she can sit down and compose as well as learn to play anything she wants to learn to play on Guitar, Bass and Drums. She's getting there with Piano, but it's a much more difficult instrument and she just started last Summer with that one; she's got a few years behind her on the others. But I bought her a full sized weighted-key MIDI piano last summer and I had 15 years of lessons, competitions and study in that instrument as a child/teenager, so I have a good understanding of typical progress in learning it. She took it to Mom's and decided she didn't want to take it back and forth but brought it back here over Christmas break. I listened to her practicing and had to walk into her room to make sure it was actually her playing rather than the computer playing back some MIDI file. In three months she's as far along as I was after 5-6 years of lessons. She doesn't even realize how well she's playing; nobody told her it was unusual for her to be able to play some of the things she's playing at her skill level. A teacher would have never had her playing those things. She just went ahead blissfully unaware of the fact that it's extremely hard to play some of the things she's learned to play and that probably made the biggest difference of all. She wanted to play it, so she sat down and learned how to play it, never getting discouraged over the fact that "you don't learn something like that until year 5." Her technique (fingering ... stop snickering) is even correct.
Both of my children love to learn new things, just like me. Except, I didn't learn that about myself until formal education was over. They have always known that about themselves.
[0] My son attends a private school that is very small and the results were the same but less surprising to me.