He wears it so you don't see his face making him scarier. At least, I'm pretty sure that's why Carpenter gave him the mask. This is also why he looks like an average man, you don't know what to expect him.
As for why the character would choose to wear a mask, watching through the original franchise, it seems he sees it as his true face as Rorschach said "give me back my face!" Remember when Micheal had that Nixon mask or w/e it was, he didn't try to kill the girl until he switched masks again. Just my thought.