The issue with that point of view is that it's based on a limited knowledge and understanding of a topic. It's a fair hypothesis but the thing about general hypotheses is that they should be updated when challenged by a more in depth understanding of the topic. In real world scenarios when shit hits the fan it isn't quite like in the Avengers when alien portals open over the street and people run in every direction. The basic shape and function of schools makes them highly compartmentalized. Short of being in a cafeteria, gym or assembly hall there really isn't much room for people to be running in all directions. Even then, in both cafeterias and auditoriums the natural response to an event like a shooting is to drop lower for cover, unless you're the shooter. Add in the fact that a single teacher shooting back at the primary person standing that has everyone moving away from is likely to end in a better outcome than not having a teacher there to do so and the tactical risk analysis tips heavily in favor of allowing properly vetted armed bystanders. In real world events armed bystanders are actually very effective with only a few cases of the attackers out gunning or police misidentifying the actual shooter.
While armed intervention is somewhat rare, it's because the vast majority of non gang related, random public shootings specifically occur in gun free zones. Take an extremely rare statistical event and then filter out >90% of events where a legal armed intervention is even possible and the data pool is close, but not quite zero. In cases where an armed bystander is present and able to engage they are highly effective. I do not have links handy but last I saw it was greater than 90% of cases with armed intervention available they were able to neutralize or impede the attacker appreciably. Now with schools, like airlines, having unique challenges that make them sensitive, I am all for offering advanced training as part of the process for allowing faculty to carry. This training absolutely should include tactics to avoid the hypotheticals you are concerned with. That being said, a large portion of people that carry every day don't just strap on a gun and go out into the world. We are the ones that do train and learn tactical scenarios and learn how to maximize defensive advantages. I don't carry a gun because I'm scared of the world, I carry one because I want to be as prepared as I can be for any situation. It's why I have a first aid kit, fire extinguisher, tire patch kit and jump start battery in my car as well. None of those things are useful without training and understanding of how they work. When it comes to guns I have had both formal and informal training in basic usage, function, repair and tactical employment. I have carried while around town in restaurants, bars, hospitals, amusement parks and movie theaters. I have also carried on airplanes and at airports and have specific training on how to defensively use a gun on an aircraft. I'm likely much more trained than the average, but I am not alone and the vast majority of my experience is purely voluntary and with the people I meet along the way I am by no means an isolated case. Armed teachers shouldn't be the primary method of preventing school shootings, but they absolutely are the best option to stop them.
Terrorists are bullies that take it to truly evil levels. They prey on the weak to force their opinions on others. A school shooter and the asshole in this news article are both evil, it's just a matter of how they chose to exert their evil on others. Who knows what his actual thoughts or motivations were, something tells me that the lack of any info on him from authorities means he doesn't meet the cliche MAGA asshole they would love to pin it on so they're just letting the shock of the crime run its course rather than diffuse what is a powerful political tool for furthering their own goals. Whatever his motivations or demographic were, he's a monster that society failed to allow him to develop those views, as a last resort I just wish that for someone that evil there had been enough of a deterrent to prevent him from trying once he got the idea in his head.