My experience with math education in the US is that they approach it as unapproachable. It is supposed to be some sort of magic, that only limited practitioners may understand, and even then only after an incredibly slow introduction. People teaching it are usually unqualified. Then if you're like me, when you get to college you get exposed to a lot better, then you wonder what those k-12 people were thinking. But a lot of people don't make it that far, because their earlier experience makes them think math is uninteresting or they'll never be any good at it.
Note that my experience involved going to a supposedly "good" school district. There is the entirely unrelated problem of schools varying in quality based on where you live.
I don't think its that easy, it depends more on the specific school and most of all on the teacher. For the record: I also had to memorize it and i went to an "european" school, or rather to an austrian one. Europe still has a wide variety of education systems.
My highschool teachers didn't (European school, too). I found it by myself one or two years later (I hated trig in the meantime) and was very proud of my achievement. Then I went to university where all the teachers were treating it like a natural thing, and that was my first glimpse of adulthood -- I started realizing I was really stupid.
Note that my experience involved going to a supposedly "good" school district. There is the entirely unrelated problem of schools varying in quality based on where you live.