Personally, I attended a private school and must've missed the warm fuzzies, because they drove us academically. No one cared if you were better at soccer or football; it was all about educational successes.
Every private school is different from public/state schools, but there are a lot more of the latter. The problem with many public schools is that they teach in a cookie-cutter fashion. If you learn differently (faster, slower, hands-on, visually, etc) you get left out--they treat you like there is something wrong with you. But it's not the student, it's the system. Many private schools can offer the specialized environments needed for those ahead or behind the curve.
In my specific case, I began at a state school where they thought it was ridiculous for a 5-year-old to be reading. They forced me to waste time coloring and painting, when I wanted to LEARN. The school had a policy against skipping grades (it was too emotionally traumatic to some kid).
So after wasting away of boredom for two years, I moved to a private school where instead of 40 kids to a classroom, there were only 20 to a grade! Each grade was set up so that the students could learn at whatever pace they could handle. Slow kids were given extra tutor time and whiz kids were given opportunities to learn things outside of the usual textbooks.
Ten years later my parents divorced and I was stuck going to a public high school. No one there had any idea what to do with me because I'd been taught to THINK rather than REGURGITATE. I was sent to the principal's office twice for "disturbing the class"... that is, I asked questions and wanted to participate/interject in the teacher's one-sided monologue. Shame on me!
Not every private school is like the one I went to nor is every public/state school full of incompetent teachers. If I were more of a sheeple I'd have fit in better in that public school. Or if I'd lived in a rich place maybe they wouldn't have had hundreds of brainless students in my grade. I just hope my kids never end up in a school of zombified conformists.