It might not be Christian in origin, but the sentiment is certainly manifested in Christian mythology. I don't pretend to be certain where the seemingly ubiquitous mindset came from, but I would wager it primarily comes from the Christian side of our primarily Christian society.
I also think that sustaining humanity is a morally neutral objective -- that is, it doesn't really matter one way or the other. If I'm on earth when it gets hit by a big ass asteroid, what good do the people on Mars do for me? Am I going to get a little fuzzy feeling at the pit of my stomach because humanity lives on? Nope, the last thing I'll feel will be burning skin.
Hindering humanity for the sake of its macroscopic survivability, on the other hand, I would consider morally wrong. The reasoning is fairly obvious.
That was my point; take it for what its worth.
