I think everyone is overstating our importance here...
First of all, "generation" is not a category that historians habitually use, and it's not one that appears in histoy texts. Can any of you say anything concrete about the "generation of 1900?" The terms does come up when a particularly demographic cohort is involved in a pivotal historical event. For example, historians will talk about "the generation of the American Revolution" or "the generation of 1914." Sad to say, none of us are involved in any pivotal events, and if "the generation of 2002" ever appears in historical journals, it'll probably be a reference to Islamic militants.
As for our depletion of natural resources, this is something thst has been going on since the end of the 19th century. We are not special in this regard, only part of a contiuum.