There are typically 3 groups of users that can add students:
Parents, using the student classroom registration page (https://[your_school].classroomparent.com/e/cr) can also add students, but they would have needed to be given the homeroom password.
Your school can also be configured to allow parents to add students to the school, and therefore their profile. This is especially helpful if you are an opt-in school, where the school system will not provide any parent contact information.