Through browsing the internet, it seems that homeschooling is common and popular in the US
I'll state this stronger than Prancer. Homeschooling is very fringe, not popular at all. As you can see from the responses here, many in the mainstream look down on it and believe a lot of stuff about it that isn't always true (but sometimes is).
FWIW most of the homeschoolers I'm aware of are doing it because they think the public school system is full of lefty atheists that are trying to brainwash kids.
I can assure you that this is not why I homeschooled my son for 2 years. As I am a lefty atheist myself.
As Prancer says, a lot of people homeschool their kids for short periods of time. Often, the issue is situational more than philosophical. In my case, my son was being shoved through to High School when he wasn't remotely ready and I had a home-based business so I could supervise him somewhat. We used a local Charter school that was all independent learning and he'd go in every 2-3 weeks to talk to his "teacher" and decide what he was going to learn next. The curriculum followed the state curriculum and they used a lot of the same books. I made him write a lot of papers and worked with him to be a good writer on top of it.
My neighbor OTOH took her kids out of school because they went to the school attached to their church with very small classes that stayed together including the teacher for the entire K-8 and she didn't like some of the dynamics of one of her kid's classes and figured they weren't going to change. (Also, I'm pretty sure she was having FOMO because a bunch of her friends were homeschooling.) They used a curriculum they bought somewhere that a bunch of her friends were using and did a lot of stuff with as a group with those families. When they moved, the kids went back to regular school. Even though they were religious, I don't think the curriculum was religious-based.
Oh and also she was one of those people who looked down on public schools and was sure private was always better; even though there are public schools in our town who are ranked very highly and are definitely better than the private schools that only exist to cater to people like her and are actually fairly mediocre.
I have other friends/acquaintances who homeschooled their kids. In all cases, something happened at school that wasn't acceptable to them so they took one or more of their kids out of school for short periods of time. Many came back to school for High School and that was always the plan. Or the situation changed and regular school was possible again or the kid just wanted to go back because he missed his friends.
-One had a smart kid who was bored at school.
-One had a teacher who picked on their son and also didn't seem to understand some of the STEM subjects she was teaching.
-One wanted a more flexible schedule for a while due to some family issues (they had to travel back and forth to aging parents, IIRC).
All of them have kids who seem perfectly normal to me (well, maybe not the super-smart one but she's weird in the best possible ways.

) and had no issues moving back and forth between homeschooling and regular school. Some homeschooled for longer than they expected and ending up homeschooling all the kids and some did it for a very short time and decided it wasn't for them.
I did know a few families through La Leche League who were into Unschooling. They were always taking their kids on trips to museums and doing projects. It was a lot of work, more than having a set curriculum IMO. I lost touch with them so I don't know how long they did it or how their kids turned out. But based on how weird their parents were, I suspect they were also weirdos. They were nice boys though so maybe not.
