Bro it's a woman, you can't hit a woman.
You shouldn't hit *anyone*, unless in self-defense. That retaliation wasn't self-defense. If the girl had been pummeling him before he started to punch back, it would be different. If he had thrown his hands up in defense or thrown a punch back immediately, it would have been the difference. But instead, she assaulted him, backed off, then he waited before basically saying "I can punch harder!" and then attacked her. They're both in the wrong and it's also pathetic that nobody nearby really helped to break up the fight.
Self-defense is what morality and the law advocate. Self-defense is not retaliation--it's not 'getting even'. Self-defense is violence to prevent further harm to yourself. By initiating the second conflict, he was exponentially increasing risk both to himself and to the girl. He should have walked away after she punched him and called the police. Yea, it's the pusillanimous individual option, but pummeling some weak-ass girl/guy/whatever isn't exactly making you look tough--you just both look pathetic. A month in jail stings worse than one of your punches ever could.
This starfish wanted a fight against someone he knew was weaker than him, and that idiot bitch obliged him. They're both richards.