Google an article called Why Do Teens Develop A Stutter, at the Speech-IRL blog. It's good overview of the reasons this sometimes happens. Short answer, the brain is still growing a lot in this period, and "developmental" stuttering (that is, not caused by medication or trauma/injury) can show up anytime until the brain is fully developed in the mid-20s. It's not as common, but it's not exactly rare either.