According to the rules of the former Aclein Academy or the current Eternal Institutions or just any other top academy, it's a formal tradition that those students who have an extreme problem with someone can challenge them as long as the latter's soul power isn't lesser than the former.
Once both parties are ready to battle, a teacher can stand as a referee for their battle. In rare incidents, a witness can also be a referee as long as he/she is stronger than the participants and has the power to stop the battle at any time.
Both of the participants then put forth their conditions and whoever loses must abide by the rules of the match. Once the match is over, then, the two must not show any grudges to each other. It is the job of the disciplinary committee and student council to take care of the situation.