My cat seems to be rubbing his face so hard on things that he is losing his whiskers and fur. Is this normal?

My cat is missing all of his whiskers over his left eye. It looks like the fur is less dense as well. He likes to rub his face on sharp things (corners of walls, tables) pretty hard. Is this safe for him to do? He'll rub his lips/gums on sharp places too which looks pretty painful.