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The problem is that no well-understood route exists from the classical world to the quantum world. No one has ever come up with a realistic quantum mechanical model of measurement (several toy models exist, and are actively studied). In the absence of such understanding, it's just a matter of splitting hairs to say either that we don't understand how quantum mechanics works, or that we don't understand how classical mechanics emerges.
This can be contrasted with the theory of relativity. Relativity violates our everyday picture of reality, but we pretty much completely understand how to recover (or derive) the classical limit. The theory doesn't give the impression of lurking secrets that quantum mechanics does.
Feynman's quote is still pretty much accurate.