by Christian Herman.
As a student you certainly can't delete an old course. If the course was deleted you'd lose access to work you previously did and so would your school.
Someone in your school must be maintaining the Moodle site. If they have not organized previous years' courses into collapsed categories or made them inactive, there's nothing you can do. At least, not without trying to find out who administers Moodle for your school and contacting them.