Most of the "homeschool" kids I've met were definitely taught to fall in line, just with their family leaders and not with their peers. Subservience to religious or parental authority is a big reason why kids end up in those kinds of situations.
It's so interesting hearing from someone with a similar experience, thanks for sharing.
The CAT exams were the same for me, always scored really high and above my grade level. I aced the 12th grade one by age 14. My parents took that as evidence that I was doing well, and I didn't trust them enough to confide just how desperately lonely I was. The CAT (and SAT) ended up being incredibly poor indicators of preparation for college level courses, many of which I failed my first semester despite also being a self-starter who reads voraciously. It was just too much of a jump for me from the unstructured way I'd been teaching myself previously, and I was missing too much background knowledge.
Even with my high SAT scores it was really hard to get into college. I ended up at a tiny private religious school (I'm not religious) because they were the only one that accepted me, and one of the few I was even able to complete the application for because many admissions offices didn't make allowances for homeschooling in their application process (this was around 2001). After a few years there I managed to bring my GPA up high enough to transfer to a state school.
In retrospect, I believe things could have been really different if I'd had access to a councilor with academic experience to explain how the system worked and tell me what paperwork I would need for college applications or what subjects would be necessary for the program I wanted to do. Even in 2001 with internet access I just wasn't able to navigate that on my own and ended up making a lot of costly (time, money, embarrassment) mistakes. And I was a pretty smart kid, I taught myself to code for one. It turns out being smart didn't make up for that much of a knowledge gap.
One important thing about child development in isolated environments is that academically: you can catch up later. You might be older than the other students when you finally get there, but you can do it and end up doing just as well as the children who had a head start. But socially that's a very long, lonely road I wouldn't wish on anyone.
The only situation in which I'd consider homeschooling my child is if it was in the daily, sustained company of other families and involved parents. Skill-building aside: seeing other kids at the playground once a week doesn't even begin to take the edge off the loneliness.
Homeschooling was detrimental to my own social development as a child, and that of my (many) siblings. Adjusting to college life made me nearly suicidal with hopelessness that I'd ever catch up either academically or socially, and none of my other siblings managed to successfully complete it. We're all doing much better now, but none of us would ever consider putting our own children through that kind of isolation long-term.
Now I'm part of an ex-homeschooler support group where most of us had a similar story. In my own case, the "homeschooling" was a political choice by parents who were deeply paranoid about the US government. They lacked the education to even understand what all we were missing and relied on a popular curriculum program to guide them without any supplemental counseling or outside tutoring.
Academically I'm sure some more educated parents could do better and understand they need to get information from a variety of sources, but socially it would be very difficult to replicate the opportunities that school provides most kids.