I don't actually know but since your getting your teeth taken out, maybe why he hole where your teeth used to be could take damage from the nail polish? It could have an effect on your nerves or something?
They want to be able to see your natural/pink skin color through the nail....an indicator blood is good/circulation....in case it's too hard to tell by your hand (tanning/blue-cold, etc)....
Just be sure to take your medicine after the teeth are pulled, my aunt died from an infected wisdom tooth after it was pulled.
omg way to scare me!!