We must be clear about this: "our" planet is dying, but the planet itself will continue to live.
This is more than semantical nitpicking. Earth is, at this moment in its vast history, hospitable to man. It was not always so, and it will not always be so.
In the incomprehensible sweep of time, the planet's features: climate, atmosphere, chemical composition and geography, will evolve until man can no longer survive here. This may take so long that ultimately it will be our sun cooling and dying that causes the earth to become uninhabitable. However, considering what we ourselves are doing to the planet, it is far more likely that our own activities will change the environment to the point where it will not support our life here.
Our time here on Earth has been ridiculously brief in the scope of the planet's existence. It has been "our" planet for a brief time so far, and will likely pass out of our "ownership" in an incredibly brief period, from a geological point-of-view. That's hard for us to grasp, since from our perspective, our time has been incredibly long. We also make the mistake of assuming that we are the pinnacle of evolution. Our spiritual beliefs convince us that it has all been created for us. This isn't the forum to argue that point, but it seems worth mentioning that this may not, in fact, be true.
Consider this: once upon Earth's time, the environment began a transition that was disastrous to life. Conditions on the planet changed, and a gas began to be released in the atmosphere. This gas was poisonous to 90% of the planet's inhabitants! Eventually, it pervaded the entire atmosphere, killing most of the living things on Earth. That gas, which we now call oxygen, is absolutely essential to the survival of at least 90% of Earth's current inhabitants. It gives one pause to consider the mass extinctions that occurred on the way to the planet becoming safe for our kind of life.
Our anthropocentric perspective leads us to make mistakes in judging extinct life forms. We speak disparagingly of the dinosaurs, using that term to label people, things and concepts that we regard as failed or passe. Actually, the dinosaurs were the most successful animals on the planet as far as we know. Our total lifespan to date is estimated to be about 70,000 years. The dinosaurs roamed Earth for over 160 million years! In fact, current science tells us that they continued to the present day, having evolved into birds. We have a bit further to go before we can begin to feel justified in disparaging them simply because we regard them as extinct. Should we live so long, to what point might we evolve? Might we, in a few hundred million years, not differ as much from our current selves as a tyrannosaurus rex differs from a sparrow? It seems likely that at the rate we are destroying our environment, we'll never get a chance to find out.
It is difficult to predict what will become of us in the future, but it seems certain that if we continue on our current course, we will destroy the environment that supports us, and perish. We are affecting the climate, poisoning the oceans, polluting and depleting the soil, fouling the atmosphere. We speak of killing the Earth, but that is merely one more sign of our anthropocentric arrogance. We are not killing planet Earth! She will survive. We our killing ourselves. Unless we change our ways, we will perish, while the Earth continues, probably in ways that are incomprehensible to us, to abide.