If we manage to kill ourselves off by means of damaging the environment, then indeed life on Earth will go on without us, but it will be very different from life as we've known it. Our absence will be a blessing to most of the surviving species on the planet. We can't survive without them, but many of them will prosper after we're gone. Our domesticated plants and animals will adapt to their life without us, or die. In a few thousand years, most of human impacts on the planet will have crumbled to dust and be mostly invisible. A new ecosystem will be established and little or no record will exist of all our accomplishments for good ... or that turned out to be harmful
What environmentally-concerned people really mean when they "Save the Earth" is something like "Save us from poisoning ourselves and destroying the ecosystem that sustains our lives." It's clear that barring extraterrestrial or divine intervention, the only way we can be saved is by our own deeds. Our children and grandchildren will have to deal with the mess we're leaving them as part of their inheritance from us. What anger and frustration might they feel for our poor stewardship of what we inherited from our forebears? We were given the gift of fossil fuels and we're in the process of squandering that legacy on self-indulgence and greed, and there are enough of us now that it's beginning to have an impact on the atmosphere and the world's ecosystems. The military is concerned about that future world with anthropogenic global warming and its associated ea-level rise. Many modern businesses have recognized the inevitability of transitioning to renewable energy sources rather than continuing the folly of our dependence on the finite quantity of fossil fuels that remain. If these very conservative segments of our society are concerned, should we not be?
I close with the following poem by Percy Bysshe Shelley: