Must you provide justification for keeping a car off your property? IMO, it's the property owner's discretion, no justification required.
But yeah, leaving aside the property rights issue, seems to me that in some schools the teachers ought to be armed in the classroom.
Agreed. No Trespassing laws are as old as the republic. If you POST your land you are justified in enforcing the ban. But if you don't post the land, especially rural land and you find somebody on your property you are within your rights to ask them to leave but you cannot take further action as long as they obey the request. But you can't have them arrested for the initial trespass as this would be the equivalent of a Bill of Attainder and unconstitutional.