When you snap your fingers, the sound is created from your middle finger hitting your palm, not the friction between your middle finger and thumb.

The ‘clicking’ sound that you hear when you snap your fingers is not because of the friction that is created when your thumb and middle finger rub against each other. Rather, as counter-productive as may seem, the ‘clicking’ sound is a result of the force with which the finger strikes the base of your thumb or your palm.

In other words, the tension that is built up between the thumb and the middle finger when you snap your fingers creates the force because of which the sound is produced as the finger hits the palm.