Can't tell if the security guy hits the girl with a closed fist or not. The girl also seems to be attacking the guy first although that still doesn't justify hitting a girl.

 ...In the video, which was shot by Forever the Sickest Kids frontman Jonathan Cook, a security guard at Detroit's Comerica Park is seen tussling with a pair of female Warped attendees, one of whom is shoved to the ground. Soon, additional security guards converge on the scene and restrain one of the females, while the one who was shoved to the ground gets back up and begins hitting the security guard. The guard responds by hitting her several times in the face.

....

 http://www.mtv.com/news/articles/1591274/20080721/forever_the_sickest_kids.jhtml?rsspartner=rssBloglines

http://www.youtube.com/watch?v=zorQyxYYNJA