I would begin with a definition of anthropocentrism. My casual definition of anthropocentrism would be a sort of human chauvinism. It is in essence the belief that humans are for some reason better or above other species. An anti-anthropocentric belief system would be one that rejects that belief system and the illogical presumption that humans are for some reason more worthy of anything than another species.
Anti-anthropocentric refers to perspectives or beliefs that reject or oppose the idea that humans are the central or most important beings in the universe. It emphasizes the need to consider non-human entities, such as animals, plants, and ecosystems, as having intrinsic value and deserving ethical consideration. This viewpoint often advocates for a more balanced and interconnected relationship between humans and the rest of the natural world.