Comment by loganmhb

I once saw an explanation which I can no longer find that what's really happening here is also partly "man" and "woman" are very similar vectors which nearly cancel each other out, and "king" is excluded from the result set to avoid returning identities, leaving "queen" as the closest next result. That's why you have to subtract and then add, and just doing single operations doesn't work very well. There's some semantic information preserved that might nudge it in the right direction but not as much as the naive algebra suggests, and you can't really add up a bunch of these high-dimensional vectors in a sensible way.

E.g. in this calculator "man - king + princess = woman", which doesn't make much sense. "airplane - engine", which has a potential sensible answer of "glider", instead "= Czechoslovakia". Go figure.