Seconding this explanation. It’s exactly right.

Rich folks can likely influence any situation but magnet != private school for rich kids.

That’s not to say there aren’t private schools for rich kids. There definitely are. But that’s not magnet schools, and it’s not where Spider-Man goes.

There was a whole scandal a few years ago where a bunch of people, including Aunt Becky from Full House, was caught paying to get her kid into Stanford. That’s university, not secondary; and maybe someone who wasn’t so splashy about everything might’ve done better. But it illustrates the point: we at least try to maintain the illusion of being meritocratic.