Isn't it a contradiction to use ways to prolong peoples lives, yet....?

While it might be ironic, it isn't necessarily contradictory even though they seem like polar opposites. Overpopulation, at least so far, is not a direct consequence of life-prolonging practices, unless you believe that modern agriculture, sanitation, nutrition, basic hygiene and other such things are unnatural life-prolonging activities. Define "natural" then find a majority of people who will agree with your definition. What exactly is a natural way of life? One in which man doesn't intervene on his own behalf? No clothing? No shelter? No tools? No education? No medicine? Where do you draw the line at what is natural and what is artificial? Don't worry though. Unless mankind directly addresses the looming specter of overpopulation, no "miracle cures" can save us from the inevitable consequences of unsustainable population growth.