Basically, the article is a poorly and spitefully-written rant against the wealthy. The argument that

They should refuse to be impressed by any opportunity that was enabled by parental wealth.

would prevent literally any achievement from being worthwhile, if it weren't implicitly arguing specifically against the rich. There are worthwhile connections to be made about the connections to IQ and GDP, and what that might imply about the average upper-class person (while avoiding social-darwinism type arguments, it would simply imply that people with higher IQ's are more economically mobile) - and considering that IQ is hereditary, what that might indicate about their children. Perhaps the children the author so lovingly calls "entitled little shits" are in fact gifted, by genetics.

His arguments about using "public money" to finance a "free education" also demonstrates some key misunderstandings about the economy (or some key political preferences of the author).

Basically, the author hates rich people and their children. And though there are key connections between the successes of children and the wealth of their parents, that may be due to factors other than the universities those children attend - the parents most likely would have been able to afford more nutritious diets during pregnancies, have fed the children better, provided them with less-stressful childhoods (low stress being implicitly found to boost the cognitive skills of children, over several studies, IIRC), and kept them with mentors and intellectuals (different from the social interaction that a lower-class child has with lower-class adults). Changing the universities would likely do very little, other than giving a use for whatever money the government takes when they tax the rich into poverty, by the author's demand. At the most, it might lessen the successes of the otherwise youngest and brightest that our nation has to offer, putting us behind on a global level.