The situation is nonlocal inasmuch as we are speaking of joint properties of spatiotemporally separated objects. We know the singlet electrons have a total spin of zero, but we cannot ascribe either particle a definite spin in advance of measurement. If you object to the word “nonlocal” in this context, fine. I would also be happy with “nonseparable,” “delocalized,” or “global.” ...He is saying that if you want an intuitive understanding of "what is going on", then you have to either accept action-at-distance or contradictions with experiment. Both of those are unacceptable.
The real issue is how to explain the phenomenology of correlations. I know that Luboš does not think highly of the EPR paper (neither did Einstein), but it is the usual starting point for this discussion, so let us focus on the most solid part of that paper: the dilemma it presents us with. Given certain assumptions, to explain correlated outcomes, we must either assign some preexisting values to the properties of entangled particles or we must imagine action at a distance. Einstein recoiled from the latter possibility — he was committed to (classical) field theory. The former possibility was later ruled out by Bell experiments. So, presumably we need to question one of the assumptions going into the argument, and that’s where we go down the interpretive rabbit hole of superdeterminism, Everettian views, and so forth, none of which is entirely satisfactory, either. We seem to be stuck. ...
If you disagree, fine. Tell me what is going on. Give me a step-by-step explanation of how particle spins show the observed correlations even though neither has a determinate value in advance of being measured.
The way out of this conundrum, as the textbooks have explained for 85 years, is to reject the idea that particle spin can be modeled by classical (pre-quantum) objects. By "what is going on", he means something he can relate to by personal experience. In other words, he wants a classical interpretation.
The classical interpretations are made impossible by the noncommuting observables. Or by Bell's theorem or several other ways the point has been explained.
When you observe a particle's spin, you change its state into something that has a classical interpretation. But just temporarily. If you then measure spin in a different direction, you are back to non-classical behavior.
The supposed nonlocality is just an illusion. The experiments only seem nonlocal if you try to match them to a classical model.
I don't know why this is so difficult. I am just saying what the textbooks have said for decades.