I feel like this isn't a great explanation of nihilism, someone might think it functionally is materialism, or some sort of skepticism.
Nihilism is the rejection of meaning, ethics, or knowledge as things that actually exist objectively. An existentialist accepts some form of nihilism, and grapples with its consequences. One key idea across existentialist thinkers is that Existence precedes Essence, that existing is always shaping who you become, rather than some kind of intrinsic being that nihilism would reject.
I agree with the sentiment of what you're saying, but I think this is actually not quite the right rule.
Some things schools teach don't really have a clear factuality, like skills. Sometimes it's hard to determine the facts, like you might encounter in high school literature class, "what did the author mean when they said this" might have multiple reasonable answers, but the author died, so we can't ask them. Sometimes there are even cases where we teach things that aren't accurate, because the nuance is too complex, like teaching 3rd graders that you can't divide by zero, because introductory calculus isn't developmentally appropriate for their math skill. Even simplifications like "sex chromosomes are XX or XY, and that makes you a boy or girl" that can cause harm if people don't learn the nuance, are an example of teaching things that aren't really accurate.
I would say schools should seek to teach kids the baseline knowledge to understand the world, and the skills to sort fact from fiction, to analyze why people say and do what they do, and continue to learn and grow in the information landscape we live in.