I went to a private school, but I was told nothing about this fact until I was in year 8 or 9, and I wasn't very well-read so I didn't "spot" it. I did notice that there was vastly more pressure to do homework, sport and so on than there was at primary school; but I was completely oblivious to the fact that it was a "posh" school.
I didn't actually start to work hard until year 11; before then I kept being told "you should be doing better" by my parents, one of whom was a teacher. I only started to like the school when I was in year 12. I did well in my A-levels, went to university with a career in mind, did get a graduate job, but found (with some regret) that that career didn't really suit me in the end.
For a few years then, I did a lot of temping, eventually decided to do driving instruction, which I loved. It needs no academic qualifications (has its own training and exams), and although my parents supported me in whatever I did, I think they were a bit disappointed that with an expensive education I wasn't doing something "academic". I did that for a few years, then I decided to move into providing A-level tuition, which I enjoy just as much. Now that I am doing this, I keep seeing how good my own education was, even if I disliked a lot of it at the time.
Speaking for myself, it's mostly that being self-employed suits me far better than being employed (mostly because I don't like being told what to do). So I'm glad I have the "choice"; but I sometimes wonder what I might have done differently if "posh schools" had been explained to me at the age of 11; I might have tried harder, but then set myself up for greater disappointment if I had failed to "do well". However, I have avoided school reunions, in case I meet peers who are far more "ahead" than I am.