Thanks for the explanation, Cunning Linguist. From a scientific point of view, it's rather complicated. And long, long ago when the compass was invented, logic did not rule supreme, probably playing second fiddle to superstition.
I came upon this discovery quite by accident after drawing the outline of a rudimentary compass on the blackboard at a lowly college to impart to my students what a compass was. The class became somewhat agitated, and on asking why they were so, one of their number responded that the arrow in my drawing should be pointing to the south. Then I told them about the arrows of all western compasses pointing northwards. Normality prevailed at that point!