I think humans should take steps to make sure we don't destroy what we already have in terms of present biomes and populations of species that exist within those biomes. It really depends on the biome you are talking about; if the conditions that cause that biome to exist on Earth cease to exist, or change so radically, do we really want a nonfunctional set of organisms on what amounts to life-support? I think we need to realize death is part of life, the two literally accompany each other as time progresses. Big-picture thinking would be the death of a species, in terms of extinction.
Humans should be concerned with extinction rates for the simple fact that if we don't, we could be ignoring conditions or factors that might contribute to our own extinction. If you believe in the theory of evolution, that man was once little better than the other animals surrounding him, in terms of thinking capacity, and then evolved into a creature capable of making intelligent decisions, how well does that speak of humans that we would ignore things that could potentially harm us?