This implies that if public schools were working "correctly", every student would qualify for "selective high schools".
First, that's impossible. People are different, they always will be, and nothing the government or anyone else does is going to make people exactly equal. There will always be smarter kids, average kids, and not-so-bright kids.
Second, why is it automatically the public school system's fault? What if something like the number of kids born to unwed mothers is a factor, like this:
https://www.childtrends.org/publications/dramatic-increase-i...
According to the above article, Black and Hispanic women are more likely to have a kid while unmarried. IMO this will have a huge impact on a child's development. And the more education a woman has, the less likely they will have a child while unmarried. Parents with more education are going to be able to help their child more with schoolwork, and it has nothing to do with how well the public school is performing.