It seems somewhat eccentric if not a little absurd to suggest that a planet is a living thing. It has life on it yes, but it’s not a biological organism. Any theory or argument that would conclude that Earth has life-like properties or even is alive could be safely put into the ‘not even wrong‘ waste bin.
So when James Lovelock and Lynn Margulis first proposed the Gaia Hypothesis in their 1974 paper Atmospheric homeostasis by and for the biosphere: the gaia hypothesis some seized on the possible implication that the Earth is a form of biological organism; the Earth is alive? Nonsense! Moreover, planetary homeostasis would appear to require foresight or planning on the role of the biosphere (the dreaded ‘teleology‘ word that biology had worked very hard to remove from the study of life). Just as worse was the seemingly fundamental incompatibility with evolution via natural selection (e.g. see Dawkins’ comments in The Extended Phenotype).
Since the early 1970s Lovelock has published numerous scientific papers and books that have developed the original hypothesis. What has remained constant throughout all of this is the that life, via its interactions with its environment, is a component of a system (the planet Earth) that can be regarded as a homeostatic system (a system that adapts in response to shocks and perturbations) in such a way as to reduce their impact. This is analogous to how you respond to changes in ambient temperature (if you are too cold you shiver and so produce heat in your muscles, if you are too hot you bring blood to the surface of your skin and sweat) so as to ensure that your core body temperature remains within quite narrow bounds.
How the Earth would do this is via biogeochemical processes (life has fundamentally affected many aspects of the Earth). Why the Earth does this is a very interesting question! In short, there doesn’t seem to be any reason why planets with life should be any more homeostatic or stable than planets without life, or that planets with life should be any more likely to continue to have environments that are conducive for life. When I say reason, I could easily say mechanism. No one has proposed any mechanism or general law or theory that could explain how Gaian homeostasis could, or perhaps even should, emerge.