I think the deputy took things a bit too far, and I definitely think it's completely outrageous that the girl was not taken to a hospital afterward (from my POV, that's the most reprehensible part of the entire incident). That being said, I feel that there are a few points that are not being taken into consideration.
Please keep in mind, while reading them, that I intend these to be taken into consideration *together*; I don't believe any one of them individually explains or justifies the situation.
1. We can't tell, from the video, how hard the girl was hit. We can tell that she was thrown against a cell wall, and there is the somewhat obscured appearance of her being punched twice while on the ground. Apparently, however, she was still conscious immediately afterward, which suggests that the attack might not have been as physically powerful as appearances suggest. This is backed up by the fact that the officer who went in second helped the first officer, and didn't try pulling him off the girl or anything like that. Veteran police officers are not raving lunatics; I seriously doubt that officer #2 was coincidentally the one guy on the force who wouldn't intervene if he saw serious damage being inflicted.
2. Many "young people" today are PUNKS. They are extreme PUNKS who believe they can do no wrong and that doing extremely stupid things - with no thought whatsoever to how their issues impact the people around them - is "cool." They are rude, uncivilized to the point of being barbaric, ignorant, and foolish, and they're proud of it. They intentionally refuse to speak or write properly, developing their own forms of slang that are completely indecipherable to preceding generations who actually learned to communicate in English. I can't believe I'm saying this, but I'm with those who previously stated that the occasional beat-down is probably necessary. We have encouraged our children to make a subculture out of shameless stupidity.
Are there exceptions? Yes, but I doubt a 15-year-old girl who's sitting in a jail cell cussing out a cop and kicking articles of her clothing at him is one of them. I really do. I'm not saying that these kids are all bad, or irredeemable, but they've been spoiled rotten with notions of "your way is the right way for you" and "you don't need to grow or improve, you're perfect as you are" taken to extremes, and extremes are needed to bring them back. These kids aren't all the product of inner-city poverty or broken homes; many of them are from the most financially secure and comfortably stationed families remaining to today's middle class. Their biggest problem in life is that mommy and daddy had the nerve to get them a used BMW for their birthday, or bought them a guitar (for their emo music) that wasn't their favorite kind.
I'm not suggesting walking around with a baseball bat to take to the head of every ignorant person you encounter at your personal discretion; however, if you're a snot-nosed, smart-mouthed little punk, and you get arrested, and you give the cop shit, and start throwing things at him, and you get beaten down... you don't have much sympathy from me. A little, yes, but not much. Grow... UP; that doesn't mean "abandon your childhood and become a short adult," it means "you're 15. Act 15, not 4."
3. Police have a job which is one of the most difficult, most necessary, and most thankless jobs in existence. Those who are serving our country in combat zones aside, I don't think there are very many people who can claim to deal with the same issues and level of stress in a week that a police officer does on any given day (stress level, maybe... doctors, firemen, etc... but I'm digressing). Policemen are human; maybe this was ignorant little punk #93 to give him lip after being arrested for doing something stupid that week, and it finally got to him after... what, eight years on the force? I'm not saying that this excuses (or even contributes to excusing), but it does make the man's actions more explicable. Maybe someone pulled a gun on him on his previous call; who knows? We don't know all that the girl herself did prior to being arrested and/or arriving at the station, either. I've seen children this age, while under arrest, scratching and biting and screaming at the cops.
4. R/E people making statements about police in general; (a) be a little more @#$%*&^ grateful for what these men and women do for you; you'd be singing a different tune if you were the one needing assistance, and (b) the police department in question has launched both a criminal and an internal affairs investigation. They are doing everything-and-then-some to figure out what happened, why, and deal with all involved accordingly.