You can easily break your hand punching someone — it’s called a boxer’s fracture for a reason — but fists work:
Although it is true that hands do sometimes suffer serious injury when humans fight, epidemiology of interpersonal violence does not support the suggestion by King (King, 2013) that the fist is a fragile and ineffective weapon. In modern societies, interpersonal violence is the most frequent cause of fracture of the facial skeleton (Lee, 2009), and the fist is the weapon that is most frequently used to fracture the bones of the face (Le et al., 2001). A Swedish study on interpersonal violence reported 63 facial fractures and 57 concussions inflicted by fists, but only eight fractures of the metacarpal or phalangeal bones (Boström, 1997). Thus, human fists are effective weapons and, when humans fight, faces break more frequently than fists.
(Hat tip to HBD Chick.)