Provocative assertion of the day:
People don't really believe in equality of opportunity.
In order for there to be true equality of opportunity, every child has to have the same opportunities to succeed.
Yet what parent among us has ever resisted the urge to give our child an advantage?
Move to a better neighborhood for its schools? That's inequality of opportunity.
Pay for afterschool enrichment and activities? That's inequality of opportunity.
Inherit money from your parents? That's inequality of opportunity.
The desire to give your child an advantage is the product of millions of years of evolution. Genes trump ideology.
That being said, we should strive against our selfish nature to provide greater equality of opportunity.
A social safety net doesn't try to ensure equality of outcomes; its goal is to provide a reasonable minimum standard of living.
The same is true for equality of opportunity; the basic education and services the state provides should be enough to allow each child a reasonable chance at a middle-class life.
Not every child can go to Harvard, but every child should have the opportunity to get a useful education. The hard part is drawing the line for that minimum standard.