We did privately educate ours, a decision in hindsight that was right. We have given her the best possible chance at life, to have all the options, whatever she chose those options to be. It's the teach a man to fish analogy. Yes we could have simply given her the money to buy a house. Or we could ensure we gave her the ability to earn her own so she didn't need it. We chose the latter. For us this was the better investment.
Her friends come from all walks in life, from the kids of our own friends to our families, to people she went to school with, and those friends are everything from very wealthy upper middle to working class and proper skint. She can walk in anywhere and fit in, be it a run down council house in a poor area to a multi million pound home and not bat an eye lid.
I grew up poor so wealth kind of intimidated me growing up. She however can sit in my fathers council flat and feel comfortable, through to her friends home, worth several million and feel equally comfortable. She has no judgement or reaction. She grew up seeing both.
Her education has been worth it, she's a straight a student with a first in law from a highly ranked Russel group,,, would she have achieved the same at state school who knows, there is no sliding doors moment. That's not how life works.
All you can do is decide what you think is the best for your particular child. For your own reasons, and do that. State school, private school, there is no one answer. It's about the child, their abilities and the options available to them.