... I agree with the conclusion, but this is idiot logic. She says "All of these sets contain people who are not school shooters", then contrasts that with "all school shooters had guns." That's a false comparison.

Correct comparisons include:

"All of these sets contain people who are not school shooters" and "Not all gun owners shoot up schools either"

or "Not all school shooters belong to any one of these sets" and "all school shooters had guns."

Her statement is like saying not all people who wrestle crocodiles get eaten, but all wranglers eaten by crocodiles are killed by crocodiles. Therefore, clearly, it's the crocodiles that are the problem, not the idiots trying to wrestle with them.