I'm British so I'll use UK examples.
Education. State schools are paid for out of tax. You can use private schools but you still have to pay your taxes for the state education you could have had. You don't get a choice about paying for a state education, even if you choose not to have one.
Health. Similar situation in health services. You pay taxes for the National Health Service, whether you use it or not, and you pay on your ability to pay rather than your demand for the services. You can pay extra for private cover but, again, you're paying twice for one service.
This is what I mean by a monopoly. You can't say that choice is being offered in either health or education when you have to pay twice to get that choice.