> Why are people in the US so against public schools?

The sentiment is not universal - perhaps not even close to a majority. Most people in the US value public schools.

As to why people want to homeschool? The reasons are diverse and differ for everyone. Themes you'll see:

- Religious parents who object to some aspect of the public school system (anti-coed, against some of the indoctrination kids get, etc).

- Smart parents who realize public schools are very inefficient and cater to the worst students. They fear their kids will not get the quality education they themselves got, and feel they can teach at a more advanced level, in a more efficient manner. If you're very skilled in certain subjects (e.g. math), it is very scary to send your kids to an average school. The probability that they will be above average in whatever subject you are good at is fairly low.

- Along the same lines, people from other countries who are great at certain subjects because their home countries valued them but the current one doesn't. That's why schools like "Russian School of Mathematics" exist. Not everyone lives in a city that has one, so ... homeschool.

- Parents who believe schools are the source of anti-social behavior and vices, and don't want their kids to end up that way. Having seen kids who were home schooled, this really works.

- Along the same lines, stuff like bullying. Especially for those who grew up elsewhere, it seems insane how normalized bullying in schools is in the US. A lot of Americans view it as a rite of passage: You go to school so you can learn skills to stand up to bullies. For immigrants, all of this means your kid learns less (whether successful against the bullies or not).

- You have ideology X and simply value a lot of things not taught in school, and devalue what they do teach.

- Culture: I had a great education, but as I have gotten older, I realized that the school/teachers alone are not sufficient - you need to be in a culture that values what you are learning. Many immigrants (and even Americans) see American culture as anti-intellectual, and that impedes what they retain (even when they learn it and get A's). They may feel the public school teaches well enough, but fear their kids will be stunted because of the culture.

I once tutored some kids, and they did not know "basic" things like number of days in a year. It's not that they were dumb, or had not been taught it. It was just a random useless piece of knowledge. They learned it, passed the test, and forgot it. And no matter how hard I tried to make it relevant for them, it wouldn't be because it wasn't relevant in their home environment or amongst their peers.

Where I grew up, it was socially unacceptable not to know this, so everyone knew it, whether a top student or a barely passing one.

You can argue that this really isn't important to know, but now extend that to almost everything they teach - including arithmetic and other parts of math. I would teach them, they could clearly understand and learn it, they'd do their homework, and then forget it until they have to prepare for the tests. And then forget it again.

You won't progress far in math if you learn that way. And those who are interested in math are often shunned. I've lived in countries where basic arithmetic (including multiplication) is a basic skill everyone (who is literate), can do on paper. They may "suck" at math, have failed algebra, but even to their old age can do multiplication and other arithmetic with relative ease. Why? Because society will judge them as idiots if they can't. It doesn't matter that calculators are available.

Someone from that country will suddenly be concerned when they see how what is unacceptable where they come from has been normalized, and what is a bare minimum back home will cause you to be shunned.

Verizonmath[1] is very much a thing in the US. Verizon was definitely not an outlier. Every since it blew up in 2006, I've noticed it everywhere - I often take photos of proper ads from real companies advertising a price of 0.99 cents when they mean 99 cents. At yard sales, it's very common to see things advertised as 0.50 cents. Outside of places like HN, when I've pointed it out, I get push back - some percentage don't even see what is wrong, and the rest insist it's OK to list prices that way, even after acknowledging the mathematical error.

If you come from Eastern Europe, you probably don't want your kids thinking it's OK. If the teacher teaches it properly but all their fellow students think it's OK, chances are your kid will think it's OK.

[1] http://verizonmath.blogspot.com/