Its not a perfect monopoly, but the market dominance of state education is greater than that of Microsoft, or Standard Oil, or any of the other companies we tend to think of as monopolies.
But it isn't a monopoly. There is no single entity controlling all of the public schools. There is no Gates or Rockefeller of education.
Each school is controlled by the state and local government, which is in turn controlled by elected officials. There are federal and government regulations, but aside from that, it is run by the people.
If you don't like what your town or district is doing, get on the school board and change it, or vote for someone who agrees with you. And if you really don't like what the state is doing, offer your own option through private education.