Well, if we take evolutionary theory for granted I can't see any particular long-term problem with extinctions, or even mass extinctions. The geological record shows that it's happened more than once due to a multiplicity of causes and life always finds a way to come back to full force; hell, I heard that no matter how deep humans have dug into the ground, we've always been able to find bacteria embedded in the rock down there (it's also more damp than expected) so we have the basics of life more or less built into the blueprint of the Earth.
Of course, whether or not we would survive is another question entirely, and I think the more pertinent one. It's not a certainty that we can afford to lose too many species before we destroy the food chains in different regions, but on the other hand the only way to feed us sustainably is to raise livestock and crops and not rely too much on the fickle vagaries of nature, so it's by no means certain that we couldn't erase most of the flora and fauna on this rock and just get by on the things we need. Might be a little bleak, but I guess that depends on whether you hold nature or man in more esteem.
I lean towards the latter; I'd never want to hug a crocodile but most children make me pretty damned sentimental and adults can be pretty decent as well. As for why 'we' started conserving the animals I think it's partly a fear that we will, in fact, destroy the environment and snuff ourselves out. Some of it's just misanthropy masquerading as a lofty concern for nature but how much is hard to say, and a lot of it is just rich, frivolous people who don't understand that people want to feed their families and build up the world around themselves, rare river newts and nice views of the mountains be damned.
