I don't think you have an accurate account of American education. Often times there is some level of freedom in high school, but undoubtedly one is forced to take classes from most disciplines. I think what changes is often the advancement one gets to (some might take Calculus, others stop at pre-Calculus or even trigonometry). But I don't think there are many high schools where one stops taking math, science, humanities, etc at all possibly with the exception of the last year. Similarly, most colleges have broad requirements beyond your major. I had to take many classes in humanities, physical, math, sociology, and other areas, for example, even though I was a cognitive science major. My understanding is that this is actually more broad than typical universities in Europe where one only focuses on their area (or certainly at least medical school is that way in many European countries).