Reviewing Bell's theorem - described in this article - has resulted in experimental evidence that all classic analogies in the style of "some state was embedded in each particle at the moment of entanglement and the measurement just revealed something about what was in that single particle locally at that time" can not be true.
Bell's theorem describes the highest possible upper bound of correlations for spin measurements along different axis if it was as you say. But it turns out that in practice they are more correlated than what would be possible according to Bell's theorem, ergo, that analogy (which, in general, is plausible and reasonable) is not compatible with the physical reality we live in.
The classical analogy don't model superposition, that's what violates Bell's inequalities, but it illustrates the correlation aspect of entanglement well.
Bell's theorem describes the highest possible upper bound of correlations for spin measurements along different axis if it was as you say. But it turns out that in practice they are more correlated than what would be possible according to Bell's theorem, ergo, that analogy (which, in general, is plausible and reasonable) is not compatible with the physical reality we live in.