Both groups cannot be right.
Actually, they can. You can disagree with the principle of private education on the grounds that it is not fair for people to be able to buy educational advantage, without ever actually looking into whether that advantage is real or just perceived (by those who pay for it as well as those who are opposed to it).
My dad would probably fall into that category - I doubt that he has ever set foot in a private school in his life because he is passionately opposed to the concept. I am also opposed to it in theory but if I'm honest would have been willing to compromise on my principles in order to give my dd the best possible start, if I had felt that the private options were better than the state options. They weren't, so (luckily for me) I didn't have to compromise. However, I was very clear that I would have bought that additional advantage for dd if it had been available, and that it would have been fundamentally unfair on those children whose parents couldn't afford to do that. I don't feel great about that fact, but I guess dd was ultimately more important to me than the principle.
The other aspect that your point seems to be missing is that not all private schools and not all state schools are created equal. Where we live, the state primary far outshines the private options, and people only really go for private at that level if they can't get into the great state school. At secondary, it's a bit more complicated, and depends on what you would prioritise, but there still isn't much to choose between them.
In a different area, the state offering might be very poor, while the private options are excellent. Or vice versa. So it comes down to my original point that it depends on individual schools and individual children. The thing that is inherently unfair about private education is not that private schools are necessarily better than state schools in every case - they are not! - but rather that the parents who can afford to pay for private have more choices available to them than those who cannot.
Of course, the state system is also fundamentally unfair because wealthier parents (like me
) can afford to buy our way into the catchment areas for the best state schools while smugly telling everyone that we don't believe in the unfairness of private education. Once again, many families do not have that option.