Which thus means that in that sense education is a right just as free speech is a right.
As to what appears to be the other question, which is, is it an American child's right to receive an education, regardless of the ability to pay,
the answer is also YES. If you say no, please list the circumstances under which an American child can be denied a public education.
No, education is not a right. Free exercise of religion is a right. In this case the education is merely ancillary to the exercise of religious rights.
Logic fail on your part.
An American child can be denied a public education if the proper legislation were passed.
I will point out that presently a very large percentage of American children are denied educations by being forced to go to local public schools.
In any case, your example is flawed. By analogy, emergency room treatment is a right because no one can be denied treatment. The fact thtat legally this is now the case does not argue for or against emergency room treatment being a right. A change in the law and this "right" would cease to exist.
That is not the case with other rights. If the city of Boston passed a law against printing the Boston Herald it would not stand up to court scrutiny because of hte 1st amendment.