The anthropocentric cultural idea that humans are active agents exerting control over their environments has been largely normalized and inscribed in practices, policies, and products of contemporary industrialized societies. This view underlies a human-ecology relationship based on resource and knowledge extraction. To create a more sustainable and equitable future, it is essential to consider alternative cultural ideas rooted in ecological thinking. This perspective underscores the interconnectedness between humans and more-than-human worlds. We propose a path to reshape the human-ecology relationship by advocating for alternative human-AI interactions. In this paper, we undertake a critical comparison between anthropocentrism and ecological thinking, using storytelling to illustrate various human-AI interactions that embody ecological thinking. We also delineate a set of design principles aimed at guiding AI developments toward fostering a more caring human-ecology relationship.