What arguments would you give to teenagers who are unconcerned about eternal life? So the kids in my catechism class aren't all that into the notion of living forever.  

That's kind of depressing, but I don't think its anything we can't get around.  However, what do you tell a kid, who is just starting their life, to invest all this time and energy in learning about Christ and His Church in order to go to Heaven at some far off date when all they want to do is grow up and live out their mortal life?

Their attitude reflects what Pope Benedict XVI wrote in Spe Salvi


  Perhaps many people reject the faith today simply because they do not find the prospect of eternal life attractive. What they desire is not eternal life at all, but this present life, for which faith in eternal life seems something of an impediment. To continue living for ever —endlessly—appears more like a curse than a gift. Death, admittedly, one would wish to postpone for as long as possible. But to live always, without end—this, all things considered, can only be monotonous and ultimately unbearable.


But even the notion of living forever is lost on them.  They were literally surprised that the point of going to Church and begin good, having a strong faith, etc... is so that we can live again with Christ.  I called it "living forever", maybe there's a better way to explain it.  I think they thought I was crazy, but I didn't think it was necessary to say, "well, you have to die first".

Somehow the sweetness and succor of heaven is lost on the young.  So how do you help to instill in kids a desire to be with Christ forever?
Unfortunately, some things that are professed in Christianity simply cannot be proven by any known scientific methods that I am aware of.  It is, for the most part, a mystery to those of us who are still living.  If the students are in a Catechism class, I would suggest simply teaching what is part of the catechism and referencing what the catechism says while also providing scriptural references.

An appreciation of the belief of eternal life that Christianity adheres to will likely come naturally in time, especially since even the young are prone to experiencing the passing of their relatives.  However, there are some activities that can be taken to nurture that appreciation.  For example, the corporal and spiritual works of mercy include such things as visiting the sick.  Prayers for the faithful departed at a cemetery may also be something that can open people's eyes to the realities of the world and help people come face-to-face with their own mortality and grow in knowledge of themselves.  Hopefully a better understanding of it comes through study and research.  All a teacher can do is instruct about what it is that is believed, not necessarily change individual beliefs.