My parents sent me to a private school for the majority of my education. They made a lot of sacrifices to allow it to happen - we had very basic holidays, never any spare cash etc but it was a conscious 'sacrifice' that they made.
I wish they hadn't and it was probably the worst aspect of my childhood. I was desperately unhappy. Really bad bullying, very elitist attitudes which I despised, and I don't believe I achieved anything more academically than if I'd gone to a state school. For me it was a suffocating experience.
When I reached 16, I told them there were two options - I'd leave education entirely, or they could support me to go to the local sixth form college. They weren't very happy because I really think they thought paying the fees and sending me off every morning was some sort of success guarantee. They refused to deal with the issues I was facing at school and confront how desperately unhappy I was.
Anyway, I ended up going to the state sixth form college for my final two years of school and it was the most amazing experience possible. I finally made friends, finally felt accepted, and achieved great results.
Unfortunately, the impact of my private school years has had a hugely negative impact on me and I try to block it out of my memory because a lot of things happened which were very difficult to deal with.
I'm aware my experience was probably particularly unpleasant and of course it won't be like this for the majority. I guess my point is that just because your child attends a private school, it doesn't mean they'll automatically be happy, or finish the experience as a more confident or fulfilled young person.
I don't have DC, but if I did, I would definitely educate them in the state system. I'd use the money saved to support extra curricular activities that they were really passionate about, or to support learning experiences outside of the classroom.