Answers:
I think this is the reason why:
When you drag nails (or chalk) across a board, the friction (stickiness) between the nails/chalk and the board will cause nails/chalk to vibrate (oscillate) just a little bit (you probably can't see it, but the vibration is there). Then, the frequency (basically how fast) of vibration will create a very high pitched sound if it is at the "resonance" frequency. (Basically, the sound will be very very loud and high pitched.) For nails, it is easy to get this frequency. If you hear chalk squeak on a chalkboard, it is likely that the chalk only oscillated for a moment to make that sound.
Some people cringe because it causes a certain part of the ear (the basilar membrane) to vibrate more at one end than the other. This can often tickle or feel slightly painful. The explanation is a bit more complicated than that, though -- this is just to give you a basic idea of what might be going on.
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