This happens notThe 6 months day/night cycle is exactly happening only at the poles (as pointed out in comments). Between the poles and the arctic circle you have a gradual change from 6 month cycle to the 24 hour cycle. Greenland is partially in this area (south Greenland, but anywhere beyond is actually outside the polararctic circle). It is happening because the Earth rotational exis is tilted, so the poles are tilted away from (or towards) the Sun every 6 months under such angle, that the Sun light in certain parts of the year does not get tointo the area beyond the polararctic circle.
See here.