The thing is there are different types of privately funded education. To lump them all in together is as nonsensical as lumping all the different types of state school in together.
The thing that I do think is true, and to answer corrie's question to a certain extent, is that a private education, of whatever type, generally means that you will have higher expectations career-wise and be more likely to walk into higher paid jobs because of your schooling.
Not because you are brighter, or better, but because your parents can afford to send you to that type of school.
Some fee paying schools are selective. Some you get into based on the good old class system/whether you are titled.
Either way, you are no brighter nor better than many children in the state system, yet by dint of birth/wealth you have a vastly higher likelihood of going on to run the country/go into a highly paid career/become a captain of industy/whatever.
And that is why people get pissed off.