Sometimes the feeling of wanting to serve others is related to your own needs (e.g. a psychiatrist or therapist who also deals with mental health issues of their own, tutors who volunteer because they were helped by a good teacher, etc.). This is not to discount the notion of vocation or calling, but to complement it. Sometimes the best people to serve in various capacities do so because their own individual stories come into play.
Maybe you do feel a calling that you are resisting, but part of the process of determining that is allowing yourself the opportunity to fully discern what the feelings are and where they may be leading you. You do not have to feel guilty about not doing anything, if you still feel wary or unsure or unqualified. Let yourself go through all those thoughts and when, after giving yourself the time and space to do that. Continue to read various sources, talk to people who do different types of service, consider the things that you have done and ponder how you felt about doing those things.

As an American GenXer, myself, I know how you might feel about society's response to service; but I think it might have to do with the focus of our education at the time of our formative years. The generations that followed us began to more often go through school mandated community service requirements that helped foster a desire to serve in a way that we did not. I know that when I worked with youth, I signed off on community service hours that they needed to complete and wondered why I never went through that as a kid. I have disagree with you on part of what you say. I think that today's youth are much more willing to fight and be activists for their communities than the "me" generation that we are a part of. It is much harder for me to get into that kind of stuff too, and I worked for religious organizations!

So give yourself a break and continue to open yourself up to what "service" might mean for you. The fact that you are even thinking about it is a good sign that you might have some kind of calling . . . and the suggestions of what that might mean that other posters have been giving are great ways to explore that too.