Apologies if I'm reading this wrong, but between this question, and casually comparing a possible origin of life on Earth to a venereal disease, it just all strikes me as very misanthropic.
My answer would be -- it's important if we deem it important, whether that's rational or not. If we start from the premise that life is good, that humans in particular are the most interesting thing out there as far as we can see, then it isn't totally bizarre that we should wish for the show to continue, extend it as far as we can. In that view, being bound to the fate of our home planet seems like an arbitrary restriction.
The value of our survival is entirely subjective. But if you value it up to the point of Earth's destruction, why would you stop valuing it afterwards?
What's a situation where Earth is destroyed and Mars is habitable? It isn't climate change, since we could just use whatever Terraforming Magic Technology we used on Mars to fix Earth. It isn't an alien attack, since they'd notice us on Mars too. It isn't war, since landing people on Mars also means we could send weapons. What exactly are we solving for here?
Earth remains more habitable than Mars even following staggeringly large asteroid impacts. As evidence, note that 25% of species on earth survived Chicxulub; those species would not have survived transportation to Mars.
And humans are well situated to be one of the survivors of a future large impact, by virtue of our tendency to burrow in the ground and to cache food. Indeed, one silver lining of the cold war is that major powers spent tremendous sums of money building fortifications with independent power and life support, as well as substantial food stockpiles, as well as numerous nuclear submarines which would weather the impact.
Another Chicxulub might kill 8 billion people, and would be an immense humanitarian tragedy -- putting people on Mars won't save us from that. But we have the technology for survivors to ride it out today.
Why is it important that our species survive longer than Earth? Honest question.
What's nihilistic about liking Earth? All my stuff is here, all my friends are here; the food is good.
Whether intentional or not, the first question implies that the extinction of the human species would not be a bad thing. The second question is a non sequitur. The accusation of nihilism has nothing to do with liking Earth, it has to do with the apparent indifference to human survival.
