Earlier quoted context omitted.
We're referring in this case to the wealth of parents, not of students. Students have very little control over which parents they're assigned.
Most students have the combined genetic material of their parents. Genetics are a key influence on aptitude. To be transparent, I personally benefited from public schools, and my parents were not wealthy (but they were graduates of public colleges). I'm not arguing that only wealthy people should have access to quality education. I'm just saying that it's a weak argument to point out that success in school is linked…
Would you like to say that the Earth is flat, disease is caused by an imbalance of humors, and Adam and Eve tamed dinosaurs for use in ancient rodeos while you're at it?
Because those would have more chance of being correct than what you're saying. Socioeconomic security correlates more strongly to educational outcomes than ANY other variable, including IQ.