There is a difference between shooting under pressure and shooting at a target practice. While some people may be able to handle this, others could accidentally kill an innocent or kill the shooter(a student). Not everyone could handle the burden of a dead student. Also, their guns could be taken by somebody else.
Also, not every teacher may be trustworthy. There are cases of sexual abusers who work as teachers to be closer to kids and teenagers. And giving them access to a gun would become a part of a bigger problem.
I am not familiar with self-defense laws in America, so someone more familiar with the subject could say if this could affect incarceration rates for teachers and to explain what could count as self-defense.
I think we all want less students dying and killing. But guns are dangerous tools in the hands of malicious and reckless people.