It seems like a simple enough question. Why do I want the human race to get its eggs out of one cosmological basket and spread to other planets? Why do I care what happens after I die? What difference does it make if the species succeeds or fails? What does it matter if we do not escape the earth by the time the sun dies? Is it a parenting instinct? A desire to see human civilization succeed? A bid for some sort of immortality?
For me, none of the above.
I appear to have no parenting instinct to speak of; apparently, that option wasn't installed at the factory. Nor am I particularly up on human civilization, which I find flawed at best and ridiculous at worst. And I don't want to be immortal though my work, through children, or through my species; I want to be immortal by not dying. :)
While I'm not particularly impressed by the vast bulk of humanity, I have a tremendus faith in the human potential: I see humanity in its current form as a beginning point, not an endpoint. I believe we have the potential to become something that is to our current civilization what current civilization is to Neanderthal civilization, and that many things we accept as a fixed and immutable part of the human condition--including death and even being fixed in the physical forms dictated by our biology--are actually not a necessary or permanent part of the definition of humanity at all.
Further, I do not see humanity as separate from the universe. I do not believe any part of the human soul or spirit comes from outside the universe; we are a part of the universe just as surely as comets, asteroids, and stars, but unlike comets, asteroids, and stars, we are that part of the universe which has the ability to comprehend itself--and to me, that gives us a value lacking in comets and asteroids.
It's not us-in-our-current-form I want to see succeed; it's those things which we have the potential to become. We have virtually limitless potential--potential that would be unrealized should life on this planet fail.
Yes, I do believe that we are not unique in the universe; there is almost certainly life elsewhere. However, it's just as probably not like us, and in all probability is extremely different from us; that means that even if we are not unique in our ability to comprehend, we still have a unique *perspective* to offer...and that, too, has value.
If Earth dies, if we and our children die, what makes it matter that some branch of humankind is somewhere surviving?
Our ability to comprehend. We are that part of the universe which knows itself, and by extension, we are the way the universe can understand itself.
This is probably an argument that either makes sense to someone or it does not, and if it does not, I do not think I have the skill to explain it in a way that makes it accessible to someone who does not feel it. But there it is.