I have yet to see a valid biblical argument for segregating a church based on demographic distinctions. Such arguments are invariably philosophical and pragmatic in their reasoning, with no clear biblical precedent or foundation. To answer the question, in a word, "no." But, every parent of a youth is, in essence, a shepherd of youth. Our vision is to facilitate the discipleship of every youth/child by the shepherd that God has already assigned them, their fathers.
This in my experience is how "reformed" Christians seem to feel over all (majority), and while I respect it, I disagree completely. I don't think a youth pastor "segregates" a Church but instead if doing his job correctly, brings it closer together. While every parent may be a "shepherd" of youth, that doesn't always happen. Also, there are fatherless children in our churches that I feel are getting ignored by many answers in this thread. I think some make the mistake of believing all church families are healthy families.
I don't assume that all families are healthy and I recognize that there are fatherless children. But there are also widows, widowers, lonely single girls and guys, etc.......should they get their own specialized pastor as well?
I think the underlying issue is differing views on the biblical parameters of a preacher, an elder and a deacon. Is there really something unique about ministering to youth compared to anyone else? Having been involved in lay youth ministry myself, I don't buy it. We all have the same spiritual condition requiring the same remedy. Much of the youth pastor idea is born of the niche-marketing mentality of the church growth movement, and the view of the pastor as CEO and therapist in chief.