Like medical care, the cost of higher education is probably not very different in the US than it is in other developed countries.
What is different is the way in which such social programs are paid for. The US has, by far, the lowest personal tax rates in the developed world. In Europe, where much of higher education costs are paid for by the government, personal tax rates are much higher.
People can debate which method is better. Regardless, it doesn't mean that higher education costs less if paid by all taxpayers, rather than primarily by the students.