This bugs me too. "The student would go to school" was not accepted, but I can't figure out why this is incorrect. If "would walk" is the intended meaning, why not caminharia? (And is there any Brazilian vs. European Portuguese difference involved?)
I don't understand the comment below that students don't go to school, but rather to universities. Perhaps that's a British interpretation? In American English "go to school" is a common and grammatically correct phrase. // We go to school every Monday. He would go to school today if he felt better. Where will you go to school next year? Does he still go to school or has he already graduated?