Washington (CNN) When the shooting started at Marjory Stoneman Douglas High School last Wednesday, there was an armed deputy on duty at the school -- someone tasked, specifically, with keeping the students inside safe.

These revelations about the actions -- or, more accurately, inaction -- of deputy Scot Peterson came on the same day that National Rifle Association CEO Wayne LaPierre spoke in front of the Conservative Political Action Conference, making a by now very familiar argument for guns.

"To stop a bad guy with a gun, it takes a good guy with a gun," LaPierre said to applause from the CPAC crowd on Thursday morning.

The problem for LaPierre is that this latest shooting in Parkland, Florida, isn't an affirmation of that view. It's a direct rebuttal.

There was a good guy with a gun just outside the school when the bad guy with a gun started murdering people. The good guy with the gun wasn't the solution. He didn't stop it.

What the Parkland school shooting exposes is the fallacy in LaPierre's argument: This is not a simple problem. And it does not have a simple solution like arming more people.

Oversimplification -- of causes and solutions -- is a major reason we have been in a standoff over how to effectively address these mass casualty shootings since they became a regular part of our culture in 1999 at Columbine High School, an incident in which there also was an armed officer on campus at the time.

Not every troubled kid who has an interest in guns is going to turn into a school shooter. And figuring out which ones will go from violent thoughts to violent actions is, largely, a guessing game.

By the same token, not every good guy with a gun is going to stop a bad guy with a gun. Why did Peterson stay outside of the school when the shooting started? And why did he remain there even as the shooter was inside actively murdering people? Was it cowardice? Did he freeze? Was he waiting for backup? Was he told not to enter the building? Something else?

We have a tendency to search for quick diagnoses -- and easy solutions -- when faced with these horrors because doing so makes us believe that these things can be prevented permanently. If we just take our shoes off when we go through security at airports, there will never be another 9/11. You get the idea.

The truth is far more nuanced -- and difficult.

There are no simple solutions. There are no foolproof answers. Mass shootings are not entirely preventable.

Latching on -- as LaPierre repeatedly does -- to the idea that if only we had more good people armed we would be able to stop these sorts of things makes it extremely difficult to make any sort of progress on this issue.

No one thing will solve the problem. Which doesn't mean we should try nothing. It means we need to smartly look into the various options and the efficacy of them. Simply because there is no foolproof solution that will end mass casualty shootings doesn't mean we shouldn't explore options that could lessen their frequency and/or mitigate the damage a shooter can do.

But simply saying "to stop a bad guy with a gun, it takes a good guy with a gun" is a totally insufficient way to deal with a problem as complex as why we have so many of these mass shootings (unlike the rest of the world) and how we can work to ensure they happen far less and cause less loss of life.

It's also not true. Just look at what happened nine days ago at Stoneman Douglas High School.

Correction: This post has been updated to accurately describe where Peterson was during the shooting.