Up until last week I had never really understood that reality is non-local because Bell's Theorem is violated by quantum mechanics. I mean, sure, I have never had too much trouble following the mathematical logic of its proof, but the pieces never really clicked into place.
What finally did it for me is to realise that the pieces of the Venn diagram one can construct for three intersecting circles are actually the description of a hidden variable theory.
I have John Preskill's excellent Caltech course (posted here) to thank for the needed kick - although he too is not explicit either.