...youth sports is one of the few opportunities that a child has to learn how to fall and get back up...

http://www.livestrong.com/article/525076-good-sports-for-young-girls/

By watching princess movies or beauty pageants, your daughter may have gotten the impression that she’s supposed to be delicate and weak. Playing a sport like baseball or softball will teach her that it’s OK to be strong. Pitching and throwing a ball is a somewhat aggressive movement, so she’ll learn to be strong and tough, without risking the injuries that contact sports like football can cause. T-ball and baseball are sports that young boys and girls often play together, so she’ll learn to be comfortable interacting with both sexes.

http://www.momsteam.com/5-7/baseball-softball-most-popular-among-safest-youth-sports

Baseball and softball are among the most popular and safest sports in which children and adolescents participate in the United States, says an updated policy statement from the American Academy of Pediatrics.

http://www.ktxtfm.org/raider/2014/05/softball-is-one-of-the-safest-high-school-sports-in-texas-but-serious-injuries-do-happen/

http://www.softballperformance.com/7-great-reasons-girls-play-softball/

http://softballisforgirls.com/2012/03/08/reasons-you-should-encourage-your-daughter-to-play-softball/