We might better understand what it is by examining the Kantian doctrine, in which we find -surprisingly- this anthropocentrism based on a subjectivism.
Indeed, Kant maintains that nothing is an end in itself, except the reasonable being, hence it must be treated not only as a means, but also as an end (it is the second formulation of his categorical imperative):
man—and in general every rational being—exists as an end in himself and not merely as a means to be used by this or that will at its discretion 1.
All the rest of it, viz. everything else than man—and beyond this, reasonable beings, (angels, perhaps?)—is nothing but means. When we know the relation that Kant establishes between value and end, we understand that it means that man has an absolute value, whereas things and other beings have only a mere conditional and relative value, relative to man, the center of universe:
The value of any objects to be obtained through our actions is always conditional. Beings whose existence depends not on our will but on nature, if they are not rational beings, have only relative value as means, and are therefore called ‘things’ [Sachen]; whereas rational beings are called ‘persons’, because their nature already marks them out as ends in themselves (i.e. as not to be used merely as means) 2.
Consequently, Kant holds this incredible idea: man alone has a value:
[persons] are objective ends, i.e. things [Dinge] whose existence is an end in itself. It is indeed an irreplaceable end: you can’t substitute for it something else to which it would be merely a means. If there were no such ends in themselves, nothing of absolute value could be found 3.
What is remarkable is that Kant uses a subjectivist argument to prove this idea, more specifically classical subjectivism, of the Hobbesian kind: value is not in the world, but it is the desire of man which creates it:
All of the ends—material ends—that a rational being voluntarily sets before himself as things to be achieved through his conduct are merely relative, for their value comes solely from how they relate to the particular way in which the subject’s faculty of desire is constituted 4.
Things that are preferred have only conditional value, for if the preferences (and the needs arising from them) didn’t exist, their object would be worthless 5.
In other words, such and such thing has a value only because I desire it. When it is not the case anymore, it loses its value. We see that here, Kant develops a subjectivist position. As to the question whether Kant is subjectivist, the answer depends on the importance given to this passage.
If we think that we find in this chapter the fundamental Kantian position on values, underlying his theory of ends and duty, then we will say that, finally, the Kantian system is based on a latent subjectivism. If, on the contrary, we think that for Kant, the concepts of ends and duty are the most important, and that we only find in this passage a secondary reflection on a less significant concept - value-, we will consider, more traditionally, that the Kantian system is a formalist objectivism, inexplicably including some subjectivists aspects; in any case, this is not the place to discuss this.
Now we see the absolute anthropocentrism involved in the creative subjectivism, depriving universe of all its value, attributing it to man, the only one capable of giving it, in turn, as he sees fit:
One claims to call into question values, reverse or transmute them; in fact, one claims to create values, since the promethean subjectivity of man is considered to have an ability which, up to now, was attributed only to God: the creation from nothingness 6.
This critique of subjectivism, as a kind of anthropocentrism and nihilism, was already expressed by Hegel, already, in a different context: he condemns the idealism of Fichte (the subjective idealism, not the absolute one). Let us see how his critique is similar to ours.
1. Groundwork of the metaphysics of morals, 2nd section
6. J.J. Goux, Where are values?