It's like saying picking up a ball from point A and putting in point B, then taking it from point B and putting back in point A is "reversing time".
If your lover sends you a left-half heart locket through the postal service, when you get it you can assume he has the right-half of the locket "faster than the speed of light". However this is cheating because to know that he has the other half requires prior knowledge of the exchange--either he sent a previous letter where he stated his intent, or you just made an assumption about the state of the environment (namely, that your partner is the only one who would send you presents in the mail). In either case, no laws of physics need be broken.
I wish people would stop posting these third-hand metaphors about quantum entanglement being like finding a single right-handed glove in your pocket or whatever. They are irredeemably flawed and completely misrepresent how entanglement works.
In this case, the question "why doesn't quantum entanglement enable FTL communication?" is properly that the reduced density operator of an EPR half is the maximally mixed state. All we can do to simplify that is to tell them that quantum concepts exist outside of classical language, and in order to understand them they'll have to learn a new language - mathematics. The most you can say is quantum entanglement enables FTL "correlations" which are stronger than classical correlations but not strong enough to enable information transfer.
[1] https://en.wikipedia.org/wiki/Language_of_mathematics
[2] http://www.cut-the-knot.org/language/MathIsLanguage.shtml
[3] http://calteches.library.caltech.edu/563/2/Goodstein.pdf
EDIT: This is not to challenge your specific assertions on this topic - on which I cannot speak with any particular authority.
Regarding the nature of language and how it relates to mathematics, I don't think it's correct to say math is a "subset" of language; there is no satisfactory definition of language that encompasses all the way humans communicate with one another, and it makes more sense to restrict the definition of language to its use in specific interactions (the language of interacting with a cashier to buy an item from a store, and the different language of telling your team what you worked on during standup, for example). In this sense the use of mathematics to describe quantum mechanics is a language in itself.
If you return a chess piece to a previous position, it's possible that doing so loses you a tempo. Even if, strictly speaking, the game/board doesn't care about the direction you move, saying it's "just" another position isn't quite accurate, since turns matter, and using up a turn to walk back a piece may give your opponent a +1 turn advantage?
For a single electron, this would not be the case.
But tracking just the ball's position is meant to analogize the fact that we have all information about e.g. a fundamental particle's position.
The simple model of a ball shifting from one point to another is a fair macro analogy because, like the quantum system described here, we realistically have all information about the ball as it moved from point A to point B.