This is the fundamental flaw with your argument. Like proving a negative, you can't teach anyone NOT to do something: only TO do something. You can try to constantly reinforce prohibition, but you can't instruct to prohibit.
With half of all American households containing guns, it is simply irresponsible to consign the children of the non-gun owning homes to total ignorance of the subject.
I imagine I could teach you NOT to put your hand in boiling water.
If you want to find a fundamental flaw with the argument that parents and not schools should be teaching gun safety, then do it on somebody else's time. It's absurd to turn your responsibilities over to the schools, and that's all I have to say about it.