The skin on garlic cloves is very sticky. It is attached to the clove by a thin membrane and shreds when you try to peel it off. Here are two easy ways to peel the skin off garlic.
First, use your heaviest knife. Separate your cloves and slice off the dry stem ends. Next, grab the handle of the knife in your fist and bring the butt end of the handle down on the garlic clove. Just give it a good pop. You don't need to hit it so hard that the clove smashes. Just a firm smack straight down onto the clove and the skin will pop right off!
Your other choice is to use the blade of the knife. Place the flat side of the blade down over the clove and smack it with your fist - just straight down onto the cutting board. The skin of your clove will come off easily. Now you are ready to chop, slice, dice, mince, press or just throw your garlic cloves in whole.