Because private schools are (usually) better than state schools in terms of exam results etc. because they have better teachers and facilities because they have more money.
So you're paying all the money to do better in exams.
Better exam results gives better prospects in later life.
Prosperity later on = send kids to private school later on.
And so the cycle continues. It basically reinforces the class system, because in order to do better in life you need to pay, but how can you pay when you don't have the qualifications because you didn't go to a private school? Poor people stay poor, middle class people stay middle class (generalising massively here, but you get the idea. Certainly, not all those who go to private school do well and not all those who go to state school are doomed to fail). So no wonder people feel disgruntled by those who go to private schools, as its a prominent reminder to them that life is unfair. People who go to private schools shouldn't be ashamed however; after all, it's not their fault they were born into a family who can afford (and want to fork out on) a good school. As long as they use their education well (working hard to get a job that can help society as a whole, as opposed to lazily working through and getting a job as some *****r banker) it's fine by me.
Personally, I think the whole english education system is poor. It's just a hoop-jumping competition which some people are better trained for than others. It doesn't really nurture intelligence.
Also, teaching is an extremely important profession that can literally mean the difference between someone doing well in life or not. Yet nowadays any old schmuck can be a teacher, and are often unmotivated or ill-prepared.
Finally, I think the character of a person is most important to doing well in education. A good friend of mine went to a sh*t hole of a state school (it's now shut down because of how bad it was), yet he still got 7A* at GCSE. He was very driven to do well, yet also confident enough to not succumb to bullying. That was the main reason he scored so high.
Conversely, I go to a prestigious private school (la di da); there are many people there who have had life handed to them on a silver platter and can't be ass*d to do anything for themselves (on a side note, it is these people who form the stereotype of anyone who goes to a private school; lazy rich cocky bast*rds who don't work hard at all, and have good exam results handed over to them by teachers. Whilst I'm sure this is true for some of the uber expensive state schools (like eton or marlborough) it is certainly not true for other private schools, and I think that should be made clear). These people do not do well because of their character (unless, as mentioned, they go to a very expensive (30k per year) school where good results are literally bought (probably, although I'm only guessing here lol!)).
Basically, education is a marathon. Private schools have better coaches, but at the end of the day, we all run the same race (and it's a sh*tty race at that).
Those are my thoughts on the matter.