TL;DR
Home school=good but often makes kids socially awkward
Public school=good for motivated individuals. You get out what you put in. Experts can help advance your thinking. Very bad peers sometimes that can be negative influence.
First off, I see that you are from Mexico. I will speak from my experience which is that from a middle class American. I don't think schools are useless. Frequently they suck, but I have learned things in school that I would not have learned on my own otherwise. I have also taken classes that were a complete waste of time. At the public school where I teach, it seems that the school is as useful as the students make it. Most of the students care more about the diploma than knowledge so they aim for good grades rather than learning the material. In high school, students get to pick most of their classes, so they can decide what they want to take and how advanced the courses will be (honors, AP, etc.). The students who really want to work hard will benefit a lot from school because schools do have experts. You will get out what you put in when it comes to US public schools. A very motivated person who works hard will be successful whether they are homeschooled or if they attend public school.
Next, I feel that it is important to mention that my girlfriend is from Mexico. She lived in Mexico City for a few years, speaks fluent Spanish and English, and is culturally both Mexican and American. She was also homeschooled by her parents for most of her schooling. She isn't weird, but most people who have been homeschooled most of their life are very weird and have no social skills. School definitely helps socialize kids. It isn't impossible to socialize them without school, but it is a lot harder. You should have them involved in sports and activities in town. They still have to interact with other children. Despite being a public school teacher, we are planning on homeschooling our children for at least a few years. We plan on homeschooling them during their middle school years because the middle schools in our area are horrible.
Yes I am from and currently living in Mexico.
I don't want to be this edgy, but, I didn't got my Diploma because i Had troubles with three teachers.
This will sound all made up, but here I go:
-My Chemistry teacher didn't allowed me to present my tests. He was an asshole with me. He always humiliated me for not talking with anyone, even though I had at least 7 girlfriends who I was with all the 4 semesters we were together. Besides I Had some male friends too. But fucking idiot. He always made everyone laugh at me in the classes. I honestly didn't cared about it as I was used to be THAT GUY who's always quiet, with good grades that everyone makes fun of for being a "nerd"
Then I won a Literature Contest held Nationally by my school and this asshole in class said things like: "Oh I just cant believe a guy like you won. Oh someone else deserved to win. Look at you, weird, quiet, with headphones all the time, You're nothing and this won't make you better"
I felt all my class mates looking at me at that moment.
-My English teacher was her daughter. I know fluent English since I was 11. And my teacher wasn't. So I was always reminding her words that she couldn't remember, or correcting her for her bad translations. Once she told me: "I want you to shut up in my classes. You've proven you're far more advanced than your room mates, so shut up"
-My Biology teacher was the Spouse of my Chemistry teacher and the mom of my English teacher: She was nice with me. She was the kind of teacher that speaks loud and screams when no one listened to her. Once she helped me with my grades, because she told me that it was unfair for me to fail my grades for missing classes. The fact I missed classes was due to health problems, serious ones.
Thanks to my fucking Chemistry teacher, I couldn't get my diploma. He gave me a "W", a "W" in the Highschool I went meant that I was so bad at that Class (chemistry) that I had to repeat the whole semester thanks to that failed class.
Of course, we spoke with the director, and he did nothing.
At that time my family and I had financial problems, so bad that we had to sell everything in our house, we almost got evicted, and we didn't ate but twice per week, sometimes once per week.
I couldn't pay to repeat the semester thanks to that asshole.
My health problems got stronger (heart disease) for not eating, and that put me in bed for months.
Then I tried to repeat the semester once we were a little better and I found out that I got kicked out from school. Literally, I wasn't registered there anymore. My grades became un existent. So I had to repeat Highschool yet again.
Of course, I fucking didn't. Got to work on my own, learnt Japanese, French, a bit of Portuguese, Italian, Russian and German.
This is exactly what I want to avoid with my children. I want them to be safe from wasting time, money, and in my case, waste and loss my health thanks to an asshole who thought it'd be funny to make fun of me.