DadTwoGirls:
I did undergrad at a very highly ranked private university where the very large majority of the other students were from public high schools. It has occurred to me that the same might not necessarily be true at all highly ranked universities. MIT and Caltech might have different preferences compared to Harvard or Princeton. However, I do not think that any of us quite knew why we got accepted while a different strong student did not.
I have been a strong advocate of doing what makes sense for you, and then finding a university that is happy with what you have done. I never did anything to get accepted to a good university. I got accepted to a highly ranked university twice (once for a bachelor’s and once for a master’s) and I think that the issue was doing well at whatever you do. You are more likely to do well if you like what you are doing.
As such, getting accepted to a top university at least for me is definitely not the reason to attend a private high school.
@DadTwoGirls If you are attending a school now, you can request to see your admission file and all the comments made during admission process. Just request to see to the admission office.