I just watched the movie "Interstellar," in which the heroes try to begin a
great question! What I might say is ask your genes (a la "selfish gene", by Richard Dawkins). our DNA seems to have built into us this force for survival, if only for the sake of our DNA ... But that of course doesn't answer your question, b/c that perhaps descriptive account of where our 'instinct' for survival/continuation might come from doesn't address the normative question of why we should care or whether we should pursue that end. Those who attempt to collapse normatively via evolution might say that's all the answer we need -- but those who don't won't be satisfied. From my perspective I agree with what seems to be your own intuition -- no good reason why we should care. Indeed, the same question can be raised more immediately: why should we care about having our own children? Of course for many having/raising children helps give their lives a sense of meaning, but that's a very selfish reason -- you have children b/c it makes your life better, but that is not looking out for the children themselves! and of course that doesn't help explain why anyone should care if a few humans escape to colonize another world ....
great question! --