outlaw corporal punishment in our nation's schools.

Schools that use corporal punishment tend to have poorer academic achievement, more vandalism, truancy, pupil violence and dropout than schools that don't use corporal punishment.
Because child abuse and its effects are becoming better understood by more people, teachers who hit children run a greater risk of criminal prosecutions and civil suits than ever before. That risk will continue to increase as long as corporal punishment of pupils is allowed.
Teachers who use corporal punishment tend to spend more time "disciplining" and less time teaching than teachers who don't use corporal punishment.
and several other reasons which will not fit here.