Government schooling is the most radical adventure in history. It kills the family by monopolizing the best times of childhood and by teaching disrespect for home and parents.
You need experience, adventure, and explorations more than you need algebra!
We could encourage the best qualities of youthfulness - curiosity, adventure, resilience, the capacity for surprising insight simply by being more flexible about time, texts, and tests, by introducing kids into truly competent adults, and by giving each student what autonomy he or she needs in order to take a risk every now and then. But we don't do that.