Not exactly. An American parent can only choose which school his/her child will not go to ... and only by opting out of the public school system entirely ... and enrolling his/her child in a private or parochial [religious] school. I did it when my daughter was very young ... and it was a very, very expensive "choice".
Strange, i thought it be universal in the industrialised countries. Do you get to choose what course packages you want at highschool?
We have a system where there are 4 profiles consisting out of courses that fit the profile, with sometimes one or two free choice courses.