The government isn't running the schools (most of the time), it's just underwriting an infinite amount of loans for students to take and go to private companies with. So if you're a University you know a) students think they should pay however much it costs to attend and b) they have an unlimited amount of funding to do so with.

Thus ITT Tech.

You do have a right to public K-12, and it's free (your taxes pay for it).

You can pay for private K-12, or "pay up" and move to a more expensive school district (read: taxes) which would theoretically give you a better education.

School districts have problems with people claiming grandparent's home addresses to attend a better school, and it happens across the country.

No such thing as a right to either because neither health providers nor educators are slaves.