It provides an opportunity for everyone to achieve, not strictly those whose families can afford it. Worse - they’re expected to contribute … even while sending their children to private institutions.
Thing is, public education is what maintains the infrastructure necessary to allow the wealthy to prosper.. still, their narcissistic entitlement causes them to resent it.
You do not educate slaves, it makes them difficult to control. And you do not like to educate your own kind because it may make you ask questions of yourself, and want higher standards, which if you are not prepared to meet them will only make you unhappy. Having said that, when viewed from Europe it is not just the conservatives, but the whole political establishment both left and right and education as a whole which is abhorrent, and the left wing will catch on in the end even in the US. Then you are in even more trouble.
Conservatives wants ignorant, apathetic citizens who are bamboozled by Republicans:
An educated population, aware of their right & responsibilities, and learning from history's lessons, is, is Not in their best interests!