He is in the wrong. I don't care what she did, she didn't have a gun or a knife. No excuse for him hitting her. He should have just laughed off the punch she threw and gone on about his business.
I am shocked that anyone defends him. I am also shocked at least one other man in the bar didn't put him on his ass when he hit her.
When I was in law school, my girlfriend mouthed off to a guy in a bar and pushed him. He should have walked away, But, he punched her back and was going to hit her before my brother and I beat his ass and put him in a garbage can upside down.