People have a tendency to forget that it's perfectly natural for animals to become extinct, and that it happens all the time - the dinosaurs died out without any help from us, after all (and chances are it was climate change that basically ended the age of dinos - modern palaeontological opinion is that is the big meteorite at the end of the Jurassic basically finished off the last few stragglers). Of course, new species evolve all the time, too. And the climate and even the chemical composition of the oceans and atmosphere have changed over time, too.
The main differences with us are:
- that farming and industry coupled with the enormous growth in our population over the last century mean we're causing effects to happen very, very quickly and on a global scale,
- that we're aware of the effects we're having (many of which could be very bad for us) and are to some extent able to predict future trends, or at least extrapolate them a few years down the line,
- that many of us are concerned about habitat destruction and anthropogenic extinction for basically sentimental reasons, which is not to say they aren't good reasons,
- and that by making policies on national and international levels, it may be possible to mitigate some of the worst effects.