A possible answer to the puzzle.

Once again, the premise n=n+1 invites us to imagine a world in which a positive integer could equal the next one. Again, this forces us to forget something we know, and the most natural form of amnesia is the one that causes us to disregard the meaning of "equals". Doing this, the sentence n=n+1 is mentally replaced by nR(n+1) for a sort of hazy relation R. And then we really do have no reason to suppose that nR(n-1) just because nR(n+1). And because equals has been replaced by something different, it feels like a cheat to subtract 1 from both sides. If you get yourself into this frame of mind, then you can say to yourself something like, "Perhaps 27 equals 28 but not 26," and experience it as not wholly unreasonable.