Organocentrism. It's not so much anthropic thinking as based on multiple huge assumptions about the essential nature of life. These assumptions are built right into many of the factors of the Rare Earth equation.
I'm pretty much in agreement with this David Darling guy quoted on the wiki wiki:
According to Darling, the Rare Earth hypothesis is neither hypothesis nor prediction, but merely a description of how life arose on Earth.[33] In his view Ward and Brownlee have done nothing more than select the factors that best suit their case.
"What matters is not whether there's anything unusual about the Earth; there's going to be something idiosyncratic about every planet in space. What matters is whether any of Earth's circumstances are not only unusual but also essential for complex life. So far we've seen nothing to suggest there is."