Everyone seems to accept that entanglement is the big mystery of quantum mechanics. I do not agree.
The favorite example of entanglement is when two identical particles get emitted from the same source, and then the spin of one is correlated with the spin of the other, even if they are far apart.
This by itself is not so strange, as the same thing happens classically. Because of conservation of linear and angular momentum, a similar classical particle ejection would also yield distant correlations.
Greene would day that the quantum correlations work differently. Okay they do. But then you have to be talking about that difference as being the quantum mystery, because if you just talk about the distant correlation, there is no quantum mystery.
The quantum spins work differently because of the uncertainty principle. The measured spin depends on how the measurement is made. Classical mechanics allows modeling position, momentum, and spin without saying how they are measured.
Okay, yes, that is an important difference, but what does it have to do with entanglement? The entanglement is just a smokescreen added to confuse you.
I did learn one thing. I always thought that the EPR paradox was named after the initials of that 1935 paper. It also stands for Element of Physical Reality. The central claim of that paper is a complete theory must represent every element of physical reality. If a measurement outcome is determined by another distant measurement, then that is such an element, but quantum theory uses wave functions instead for the dynamical theory.
Again, the real mystery here is the uncertainty principle, which implies that the measurement outcome depends on how the measurement is done. The fact that there is a distant correlation would be true about any theory.
Nobody thought that 1935 paper was any big deal until Bell showed in the 1960s that the quantum correlations could be quantitatively distinguished from the classical correlations. He also renamed the elements of physical reality as beables. He wanted to follow Einstein's dream of having a theory based on beables, like classical physics, instead of wave functions. The Bell test experiments proved this to be impossible.