It's a good question as to why the wealthy send their kids to private schools.
In many cases, I think there is just an assumption that private schools are better, perhaps because people look at results without also looking at the cohort. However, bright kids can do just as well in state schools.
In some cases, I think people believe that they're buying access to a better peer group, ie less disruption etc. Not necessarily the case!
Some people are attracted by the wide range of extracurricular activities on offer, or lots of sport etc. But there is no reason why these can't be facilitated outside school if a parent is willing.
Some people believe that private schools confer confidence. But again, nothing that can't be developed and nurtured by a canny parent facilitating access to a range of opportunities.
Some people value the network that private schools offer. That may be valid in some cases, but only where the parents don't already have a wide network of their own.
Some people are attracted by the nice environments and superior facilities in private schools. This is fair enough, I suppose, if you prioritise that kind of thing.
Some people value the longer school days/one-stop-shop approach to extracurricular activities because it fits around their work commitments etc. Fair enough if that's what suits them.
Some people feel that their kids are struggling either academically, and that they would benefit from more attention/smaller class sizes etc. Fair enough if they feel that's what their kids need.
Some kids feel that their kids are struggling socially and that they would benefit from being in a smaller, more nurturing environment. Fair enough.
Some people feel that their kids lack self motivation and would benefit from being in a pushier environment. Again, fair enough.
Some people feel that their children's SEN will be better supported by a private school. Fair enough, if they have researched this and found it to be the case.
Some people have significant concerns about the specific state schools that are available to them, and choose private schools as a last resort. That may or may not be valid, depending on the schools in question.
I think there are lots of different reasons why people might choose to go private, but not all of the reasons are equally valid imo. And not all kids would necessarily benefit. Some kids thrive within the state sector, and simply don't need any of the "extras" that private schools are able to offer.