We are trying to preserve populations and environments because the comfort and decency of our present lives, and those of fellow species that share our planet, depend upon such stability. Mass extinctions may not threaten distant futures, but they are decidedly unpleasant for species caught in the throes of their power. At the appropriate scale of our live, we are just a species in the midst of such a moment. And to say that we should let the squirrels go (at our immediate scales) because all species eventually die (at geological scales) makes about much sense as arguing that we shouldn't treat an easily curable childhood infection because all humans are ultimately and inevitably mortal.
We can surely destroy ourselves, and take many other species with us, but we can barely dent bacterial diversity and will surely not remove many million species of insects and mites. On geological scales, our planet will take good care of itself and let time clear the impact of any human malfeasance.
Stephen Jay Gould
1941 - 2002