I went to public school. My parents were blue-collar workers, but they were always home in the evenings. I had a very good family life. My closest friends in high school weren't extreme achievers, but they were damn level-headed, and I'm very thankful for that. I'm currently a software developer with a $100k+ stash and growing, and I'm very fortunate and blessed to be where I am. Absolutely none of that required private school.
Back in high-school, people were freaking out about grades and extracurriculars so they could get into "the best" colleges. If we think it's bad in the US, I've heard it's far, far worse in Japan - it's worth looking up. Why people in first world countries are so terrified of their kids not getting the very best of everything seems like the very worst kind of hubris in all of human history, but people let the quest for prestige infect them no matter where they're at, I guess.
I did honors and AP classes, was even in NHS, but, after a few transfers, basically ended up at a 4-year community college (that's my description, I know it's not a real thing :) ) and completed a not-so-lucrative degree. Yet things still turned out for me. I would change some of that if I had to go back (I'd get an associates in a well-paying field and enter the workforce to save for FI immediately), but I tell you what, my parents just being around and being loving and supporting made a world of difference to me. Sadly, some of these parents who are obsessed over their own child's "success" spent long hours in the office to afford stupidly priced sh*t (like most private schools, IMO), and then wonder what happened when their kids make really bad decisions in life. There are always exceptions, of course. My parents are simple people, too. If you need extreme success, it's because you haven't learned contentment, and I guess when people run out of things to worry about, they start worrying about their children's education, and the situation you're describing happens.
I've also noticed that pre-schools will often be given academic/British-sounding names. Goddard School. Princeton Academy. No doubt to invoke imagery of prestige and "high education". It's pre-school dammit. But anything to convince parents that the formative years of education will get them into top schools over a decade later, and into a top life, so pay us money. Ugh. Makes me sick. If you really love private school, hey, it's your money, but mostly people are trying to sell you a lie. Stupid is as stupid does. Private school does not equal success in life.