They don't. In this image (from 28th Dec 2021) the blue grid represents lines on an equatorial grid. The lines that run from top right to bottom left are North-South lines. The tips of the crescent very clearly don't point to the North.
The moon is lit by the sun and both the sun and the moon are in the plane of the ecliptic (to within a few degrees). So, as the "bulge" of the crescent points towards the sun, and along the ecliptic, The tips of the crescent will point towards the ecliptic pole which is about 23 degrees away from North.
However since the moon is not exactly on the ecliptic even this is not exactly correct, and close to new moon the tips of the moon could point almost anywhere (think how the invisibly thin cresent will rotate as the moon passes the sun on a new moon at which there is no eclipse.)