Christ centered missional service of and by teenagers should absolutely be focused outwardly.
Yes, even teenage bodies are God's temples and the Holy Spirit dwells within those who trust in the Son of God. (How the God of the universe can tolerate living inside a sweaty-pitted pubescent is one of the great mysteries and mercies of this age.) The Holy Spirit, however, is not a meek firefly trapped inside the jar of their rib cages. He is the all-powerful Spirit of the living God graciously given to us as the great Helper and Comforter. He can equip even the most annoying and immature of our belching boys to actively take part in the great commission--making disciples of all people, baptizing them and teaching them to obey everything that Christ has commanded us. Youth ministry cannot fulfill the great commission without an outward focus.
Good youth ministry is fixated on our living God and His lofty mission. Christ followers are missionaries whose focal point is outside themselves and whose resources and energies do not terminate on themselves. In this calling, leaders and adolescents vigorously, boldly and urgently pursue together God's reconciliation of this broken existence. We have been given the glorious opportunity to see students witness and participate in the salvific action of the Holy Spirit in our communities, churches, friends and even our adversaries.
Youth Ministry is Focused Outward on Cultivating Servant-Hearted Biblical Community
In a true biblical community everyone is free to focus all of their attention on the needs of others and very little on their own. Youth ministry communities of Christ followers should never be a collection of teenage human individuals who are parasitically demanding to have their own individual needs met. The satiation of one's individual desires should never supersede the effort to meet the needs of the community.
In a servant-hearted, biblical community, energy doesn't have to be selfishly wasted on the worrisome concern for an individual's own needs because everyone else in the community will be concerned about their needs for them. The model that Christ has given us is one of humbly serving others and humbly accepting that same level of service from others reciprocally. That is why Christ calls us different members of one body. Sure, in my body my stomach garners more attention than, well, any other part of my body, but that favoritism does not hold true for members of the body of Christ.
Youth ministry helps students see beyond themselves, to lead by serving, and offers them a community that shares all good things, from pizzas to prayers, without prejudice so they no longer have to worry about themselves and can be freed up to be concerned with the needs of others.
Youth Ministry is Focused Outward on other "Churches"
This may surprise you so please sit down and hold on. In your city, God does not work exclusively through your church. Good youth ministry understands that there are other believers, even in your own neighborhood, who don't attend the same "church." These men and women are our brothers and sisters and they are on the same mission that we are on. Youth ministry, in its outward focus, should be forming partnerships with these churches and organizations so we can better reach our city with Christ.
Do you know who does know the students from other churches? Your students. They go to school with them and they hang out with them all week long when they're not with you feigning attentiveness while listening to your "when I was in high school" stories. An outward focused ministry takes into account the work God does in an entire community all week long through many churches and they intentionally leverage Christian partnerships for the sake of the gospel without a spirit of competition.
Most of all--Youth Ministry is Focused Outward on the Lost
The whole of the student ministry--be it parents, professionals, volunteers or the students themselves--should be consumed with an urgency to boldly declare the gospel to the thousands of non-believing teenagers in each of our communities and our world. This must be our priority and our driving force. It must be because it was, and still is, Christ's priority.
To use a variation of Christ's parable, if we have 99 students involved in our youth ministry who are fully devoted followers of Christ and there is one student anywhere who is "lost," just one we know of who does not know Christ, then our mission is to give every ounce of our caramel macchiato enhanced energy to focus on the one who does not have true faith. An outward focused ministry understands that our churches should not be exclusively catered to the students we "have" but more on mission for the ones we "don't have."
Our approach to the lost cannot be an inward focused strategy of making more attractive programs, better formatted invitations or the tried and true method of bribing more attractive and popular teenagers to attend your bible studies. Outward focused youth ministry is the real, laborious and uncomfortable at times, work of investing and intervening in the lives of those who don't trust Christ. We must ourselves be active in participating and training teen believers to identify and love the lost by graciously giving the gospel.