Cats are mammals and all mammals have at least some fur --even naked mole rats! Most mammals have lots of fur, however. Fur (hair) is a little bit like a leaf on a tree--ultimately hair and leaves die and fall to the ground. The hair that gets caught in the brush you rake over your head in the morning is the product of this shedding process. Because cats have a lot more hair than people do, the shedding process is much more noticeable. So...your excellent question should be reframed --why do mammals shed their fur, since cats are not special in this regard?