Should the cop have punched her? That is left to be seen and determined by his superiors. We have too much instant cam with phones. And as it has been pointed out, we only saw what the person filming wanted us to see. Can you notice how large the crowd is around him?
He was more than out numbered and I saw at least two or three phones aimed at him to record his every move. I also know how hard it is to calm a girl that is that age down. I have had to hold one younger than that back when she wanted to beat the crap out of a boy in my classroom. He had it coming don't get me wrong, but I did not want her to get into trouble for throwing the first punch. She about threw my shoulder out in the process. She was beligerant and kept saying what are you going to do about him? I told her I could not deal with him until she calmed down! Finally she stopped. They both had to go to the office, but I pleaded her case considering he was making racial slurs to her. She did not get into trouble, but he did. If she had just let me deal with him, she would have never gotten into any trouble. She was just told to let me deal with students who are out of line. My shoulder ached for a week. And she was calmer than these ladies. It was my first day of class.

I have had parents get angry because you "touched" their babies. The baby in question was choking the life out of another kid. So I slid my arm between them and pulled the boy off of the one he was choking. I told the parent I had two choices, touch her baby, or let him kill another student. I chose to keep him out of jail, and save the students life he was attacking.
Teachers and policemen are having more and more problems with combatitive teans. Teachers are not trained in hand to hand combat. On the contrary we are to try and control situations without it escalating that far. I have seen teachers hit over the head with chairs because they were trying to break up a fight between two girls.
The NAACP look for any reason to jump into the fray and defend the african american girl. It doesn't matter what she did in the first place. They will get involved because they get free press over it all. Sometimes we need to hang back and get the whole story. I am sure these two girls behavior was far from lady like, and if they had just remained calm, listened to the officer, it would have never escalated to this level. I don't defend the policeman for punching the girl, but I was not there, and I don't know how bad it was for him.