He grabbed her first arm (her right) defensively to stop her from trying to hit him (I have done the same move). She was waving that fist at him and obviously threatening to hit him with it.
He is under no obligation to allow her to land a punch before reacting. He saw a threat and tried to neutralize it by grabbing her right hand. He then continued to try to calm the massive woman down (who probably had 20 pounds on him) but she escalated the situation further by then trying to left hook him to the jaw (which he dodged). Having had enough of this massive drunk woman continuing to attack him he finally pops her in the jaw and walks off.