From wiki (link above):
Anthropocentrism is either the belief that humans are the central and most significant entities in the universe, or the assessment of reality through an exclusively human perspective. The term can be used interchangeably with humanocentrism, while the first concept can also be referred to as human supremacy. The views are especially associated with certain religious cultures.
I think of anthropocentrism when I have discussions with theists regarding evolution. There are a number of traits that exist (like intellect, speed, strength, climbing ability, climate adaptability, etc), and we are the best, for all intents and purposes, at some of them, but lacking in others. These traits allow different species to adapt and excell in different ways. There's no right or wrong. There's no superior or inferior. It's all about adaptation, propagation, and survival.
Yet people hold our specific attributes to such a high regard, and really, I find that to be nothing but anthropocentrism. I don't see the justification for the view that we are superior. Our intellect is as useful to us as is the ability to play dead, pose as a log, camoflouge oneself like chameleons do, etc to other species. Yet people state that we're so superior, and they use intellect, the thing that we happen to possess (convenient, much?), as the indicator of this.
To me, this is just a self serving viwepoint, borne of a pre-existing idea, and supported by taking one attribute from a field of many equally useful (in the right circumstances) ones and arbitrarily proclaiming that particular attribute to be of the utmost importance or usefulness. And why is this determination made? How is it supported? Why? Because we possess that trait!!! Isn't that just wonderfully circular?
It's circular, it's self serving. It's anthropocentric.
At least in my view. Feel free to disagree (or heap praise upon me!).