It's that typical thing of sending thick people to very expensive schools. It doesn't produce geniuses, it just produces very confident idiots.
It's interesting you should say this. I was 'fortunate' enough to be schooled at a reasonably expensive school (not a very expensive one, mind), largely for the better quality of teaching. Having previously experienced the teaching quality at the local comprehensive, I can confirm that this was undoubtedly of better quality.
However, there was an atmosphere even here whereby achievement was measured not by academic success, but by who you were, and how well you did on the sports field. For instance, the head boy in my year just happened (purely by chance I'm sure) to be the son of the school's bursar (which is a posh word for accountant). Even in a relatively unknown private school, there was a culture of preference towards 'breeding' - in other words the posh boys got away with whatever they liked and were handed privilege on a plate.
At the time, I thought I was lucky to get a better quality of education than the masses, but in hindsight, the whole experience really just illustrates how private schooling feeds social division. The money pumped into such schools would instead be much better spent on giving the same level of education to all, so that those with the greatest ability get the support they need to achieve to their potential, instead of, as stated above, ending up with more very confident idiots.