We are not excluded from nature - extinction for almost all species is part of nature.
I suppose the main difference with humans is that technology has distorted nature - and ultimately wars will occur when food/fuel availability drops. We can see that happening already in the world and we can see the human tragedy in Dafur.
I think that ultimately when things get really bad for the western world, ie. poverty and starvation, not to mention malaria creeping to northern latitudes (as it is already), war will become a bigger fact as the consuming western society go out to grab what they can from other countries. At some point someone will get nuclear capability and some sort of apocalyptic end will happen.
Incidentally I do see humans as evolved from primates (no problem there - I like bananas) but when you say:
I find it difficult to understand how it is so easy for you to deem human beings worthy of extinction while at the same time defending pests that, without keeping their population in control, will damage nature even more.
I think you miss my point in two ways:
First, I don't deem humanity worthy of distinction, it is just an inevitability in the natural course of events. Practically every species that has ever existed has become extinct, and very few have lasted more than a few million years. Why should the human species be any different to others?
Second, how do 'pests', as you call them, damage nature? They are part of nature - the only thing that they do 'wrong' is to damage human interests. I think Canada would be a lesser place without its otters, bears and wolves but go to Scotland where they were once prevalent and find a single example - they have all be exterminated. That is not nature it is barbarism and in this day and age we should be moving away from such practices rather than endorsing them.
If you want to take a religious view of this issue (personally I don't because I can't see how religion is relevant to life) then in the Judeo/Christian/Islamic tradition it is generally believed that God gave mankind dominion over the creatures of the world. Surely with dominion comes responsibilty - not just a right to obliterate. If I believed God existed I would have to wonder what he thinks of what human kind have done to creation - it isn't exactly an encouraging sign of respect.