As someone who has attended a private school and a state school, I'm inclined to disagree with you on a number of levels.
Academically, private schools are superior (lets not get all butthurt and call me elitist, because I'm not). They have better resources and small class sizes that allow more teacher-student contact. For many people, who need extra help this can be hugely advantageous, and promote learning in a way the state sector cannot. This isn't the schools fault, and in no way am I suggesting that, but private schools help people who need extra support academically. Furthermore, they have the facilities to expose the child to a wider range of academic disciplines, that in a state school would just not be possible.
Secondly, pastoral care is much better at private schools. I was bullied a lot at my old state school because frankly the teachers didn't care as they just wanted to get paid. In private schools, there is very often a zero tolerance policy on bullying and people may be suspended on their first offence, which greatly discourages bullying amongst children and makes the learning environment safer and friendlier and thus more enjoyable.
Finally, private schools offer a holistic outlook to learning which makes it's pupils more rounded individuals. There is greater access to clubs such as MUN, debating, charity work, a greater range of sports and skills you would never find in the state sector, such as specialist instruments. Private schools are more likely to promote that pupils engage with their professional interests, through law and medicine societies, for example.
I'm not saying it's fair some people have a better education that others, I'm just saying you can't slam all private schools just because some people can afford them and take advantage of the oppertunity.