Overuse injuries are responsible for nearly half of all sports injuries to middle school and high school students. Specialization is a logical culprit. A report this year by the sports medicine department at Loyola University of Chicago found that "kids are twice as likely to get hurt if they play just one sport as those who play multiple sports."The exponential increase in youth sports injuries has led the American Orthopedic Society for Sports Medicine to help launch StopSportsInjuries.org, which is a website devoted to educating parents and youth about sports injuries.
A related problem is burnout. It is not uncommon for kids to dedicate themselves to one sport starting at a very young age, and then reach their junior or senior year of high school and not want to play anymore. Or, I am aware of instances where they had actually earned scholarships to Division I programs and decided they no longer enjoyed playing ("On Athletic Success").
One of the sources quoted in the article encourages young athletes not to specialize until they reach high school. Personally, I don't think they should specialize until college (if they get that far: less than 1% of high school athletes get a Division I college scholarship and only about 5% go on to play sports in college). Kids bodies develop at different rates, and they may not excel at a particular sport until "late" in their careers (e.g., I played college baseball with someone who went to college on a golf scholarship). But, if they've already given that particular sport up, they'll never know.
Bottom line: Encourage kids (1) play as many sports as reasonably possible (we don't want their parents to be run ragged); (2) take breaks from every sport they play in order to avoid injuries from overuse; and (3) don't specialize until college. It's pretty simple.