For example: Stuyvesant is a public high school. But is it actually? There's a 3 hour test you take in order to be admitted. 900 or so kids are admitted. How is this "public?"
There is nothing wrong in segregating kids based on their ability. Public universities use tests to take the best kids and this should happen at all levels. A black kid who is smart should not be held back just because he lives in bad neighborhood. He should get into a better school if he can score more.
Yes. That is how it happens in urban India. Even for nursery admissions schools interview both the kid and parents to see if they have potential.
You are right, he should. But he is statistically very much likely not to based on his upbringing and systemic discrimination.