I'd like to point out two additional potential explanations. 3) Children born to wealthy parents are more likely to go to better primary and secondary schools

I'd like to point out two additional potential explanations. 3) Children born to wealthy parents are more likely to go to better primary and secondary schools (possibly private schools, or possibly by living in better neighborhoods.) This generally leads to smarter people as mentioned in #2. 4)Secondly, wealthy (or even middle-class) parents are more likely to have a culture of appreciation for education, as education likely played some part in getting them to where they are, and that culture will tend to rub off on their children.