Because it’s possible to do things that would be impossible with a hidden local variable theory such as you’re describing. See Bell’s theorem or https://en.wikipedia.org/wiki/CHSH_inequality, a game at which a quantum strategy can beat any classical strategy.
And see also Sidney Coleman’s “Quantum Mechanics In Your Face” lecture (youtube, transcript) which walks through a cousin of Bell’s theorem that’s I think conceptually simpler—for example, it’s a deterministic result, as opposed to a statistical correlation.
Because it’s possible to do things that would be impossible with a hidden local variable theory such as you’re describing. See Bell’s theorem or https://en.wikipedia.org/wiki/CHSH_inequality, a game at which a quantum strategy can beat any classical strategy.
And see also Sidney Coleman’s “Quantum Mechanics In Your Face” lecture (youtube, transcript) which walks through a cousin of Bell’s theorem that’s I think conceptually simpler—for example, it’s a deterministic result, as opposed to a statistical correlation.
There’s also a 3blue1brown video on Bell’s theorem: https://www.youtube.com/watch?v=zcqZHYo7ONs