What are the reason for not allowing students to bring mobile phones to school?

Reasons are different for every school but the main reason would be because they can become a distraction and a problem for students. If a kid is playing on his phone in class then the teacher must stop the lesson to either take the phone away or tell the student to stop playing on it. Most schools I know allow phones in the school but if your school doesn't allow them they might just not want to have another thing to prevent kids from learning.

Students might take them into locker rooms or bathrooms.  This would allow them to inappropriately use their cameras and social media.  Then there is the issue of cheating in the classroom using text features during a test or quiz.  More importantly, bullying is the main reason phones have been banned in schools. Students have not mastered the control factor inside and outside of school.  Cyber bullying is still and issue that needs to be addressed before schools will completely allow total unrestricted phone usage.

Iwould say you should mainly cover the areas about how it has no health issues or concerns, and also cover the cost, and benefits.