If this generation dies, it dies only because of its own stupidity. Because it doesn't care about scientific research in the area of life extension. There is some research going on, but it's pace and the amount of funding is ridiculous compared to the importance of the goal.
It is possible that folk in middle age today, myself included, won't be able to take advantage of rejuvenation biotechnologies - if, for example, development continues to be funded poorly, broader public support for the reversal of aging fails to emerge, or the first thirty year cycle of research, development, and commercialization fails to produce meaningful results. As Aubrey de Grey notes, minimal levels of funding seem to be the most obvious and plausible blocking issue for the foreseeable future. The young have few such worries: they have time to wait out failed business cycles, slow-moving research, public opposition, and an economic collapse between now and when they would absolutely need rejuvenation therapies. A good fraction of the children born in the past few years will live a thousand years in youthful health and vigor, thanks to an upward, accelerating curve in biotechnology.
So from my perspective it is indeed the case that the only way today's young folk will die of aging is if they choose to do so - such as by failing to support the goal of engineered longevity because they believe that people should age and die, or because they haven't given much thought to living a life any different from that of their parents and grandparents, or because they choose to remain ignorant of medicine and its future. Those are all choices in the broadest sense, and possibly stupid, though it's worth considering that actual stupidity and mere lack of attention given to a particular topic look much the same from a distance.
Few of us pay more than a tiny amount of attention to anything beyond our specialties, but this is one of those rare eras in which a great deal hinges on paying attention to a specific field. The future of biotechnology has to potential to reshape and greatly extend all of our lives, and remaining ignorant or on the sidelines only adds to the chance that the necessary advances will arrive too late for us.