Because carpet is soft...
The carpet may be soft, but your chin is a very sensitive part of your body. It never comes in contact with anything - unlike your hands - and it never builds up callous or protective tissue. It is also home to a lot of receptors - so when you rub your chin against the carpet, you are giving it a friction burn and that hurts. Not sure why you might want to rub your chin against the carpet in the first place, but that's why it hurts.
