Long-standing Western philosophical concepts make the claim that individuals have a right to live their lives for their own sakes.
Just because they're long-standing doesn't make them absolute. Mythopoeic ways of thought prevailed for millennia, but were eventually overthrown, not because they were more or less wrong than rational ideas but because of natural meme selection - cultural evolution, if you will.
Renaissance and Enlightenment homo-centric ideas are going very much the same way already, along with Neutonian physics and Christian morality, and without the help of radical environmentalists.
There is no getting away from the fact that humanity is neither more nor less significant in its own right on the backdrop of life of the planet than any other living organism, from the dinosaurs to the common earthworm. The human race is only here because it claims as its ancestor a particularly ungainly semi-reptilian, semi-mammalian creature which narrowly escaped extinction by evolving the ability to exist on the refuse of others. Not exactly exalted ancestry.
This is the next step in the evolution of the existentialist meme - first we come to understand that the human condition carries no inherent meaning, and now, through scientific contemplation of the world around us, we come to recognise that it has no objective (well, scientifically speaking, anyway) value.
Face it - if you want to be a rational, logical, scientifically minded person in the 20th century, you can't cling to medieval notions of the importance of Man. Personally, I have no such ambition - the purely scientific is too stark a vista. So, for myself, I believe in God, the faeri, Gaia and pixies. Which is fair enough, as long as I don't go about claiming that I am inherently, objectively and absolutely correct, or try to refute the ideas of others on the basis of their incompatibility with my own doctrine.