School Responsibilities
Of course there should be a class, or classes, on personal financial management in high school/junior high/middle school.
It should probably be a significant portion of education as long as education is publicly administered. It's one of the most important life-lessons to learn -- more important than any "classic English literature," or learning a 2nd language, or trigonometry, or calculus, or chemistry, or biology, or history, or political science, or psychology, or religion.
Financial literacy deserves more educational focus than really almost anything but the most basic math and language and that's only because basic math and language are a prerequisite for financial literacy.