Human Chauvinist

I've read that people, formerly ordinary everyday mundanes of normal people perspectives, who are experiencing some kind of awakening to the plight of the world move away from anthropocentrism (human chauvinism). As they do, supposedly, they have a moment where their thinking shifts from “I'm saving the planet”, to, “I'm part of the planet fighting to save myself.”
This begs the question, at least to me: What does it mean to be an anthropocentrist and have always held the view of one-self as part of the planet, not apart from it?

I've never seen myself as apart from the planet or the rest of the world. I am still terribly fond of human beings and our accomplishments, and my aim in life is to further my species. Until the day some big bad mother of a species comes along, wipes us out and builds his outhouses on our bones, I plan to continue holding that view. As a part of the world as a whole.

Doesn't mean I undervalue any other species or thing on Earth. I try very hard not to. I just think that, generally, we're wielding the biggest swinging cods this side of the viruses. No reason not to feel at least somewhat accomplished over it and try to keep it so – That's what the whole affair is about, isn't it? Thought so.

What good is a species that isn't wired to think highly of itself?