There is not one simple answer to this question.
In fact, the reasons why young people should influence policy are essentially enumerable. Still, this article from Tufts University's Center for Information and Research on Civic Learning & Engagement goes a long way to explain just how important youth voices are in shaping policy.
As discussed in the article, there are a few main merits to youth engagement in local policy. First off, young people share many important features that grant them special interests in certain policy areas. For example, although they may have diverse opinions on the matter, all young people share an interest in effective and accessible education. Young people also bring special knowledge to the policymaking table. Few people have as good an understanding of local culture as young people. Similarly, young people have a special talent for picking up on the most pressing social issues of the day.
To learn more about why young voices matter, read the article linked below.