Public doors and places with a lot of people open outwards to meet the fire code. If there is a crowd at the door there is no space to open it inwards.
For armed teachers, what it would take is acceptance from the teachers union, it being voluntary with tax credits for the purchase of the gun, holster, ammunition, and classes along with paid time off to attend training. There would also need to be liability protection.
For training they would need to take basic pistol, 2 day CCW course, and 1 day scenario training. Have an annual qualification course similar to security guards and refresher training. This would allow them to defend their classroom and the immediate area outside.