It's unfair to characterize deep ecology that way. Although Naess--whom I know only by reputation because his work is neither widely available nor translated--is hardly an outlier; Charles Darwin, John Muir, George Perkins Marsh and H D Thoreau deconstructed human primacy quite convincingly over a hundred years ago. 

Evolution was not a process that culminated in the creation of our species. We're merely another evolutionary wrinkle in a process that started billions of years ago and will, hopefully, go on long after we homo sapiens exist the scene.  In nature--where humanity lives--a population boom that exhausts resources precedes a massive die off.

The predictions of the Club of Rome to which you're alluding relied on computers that were in their infancy, as did the few predictions of  a coming ice age that deniers like to tout. And predictions of adequate resources for all you make do not account for the impact on climate and living ecosystems that human actions are causing.