The world has survived for billions of years. It's been battered by asteroids before, it's experienced countless earthquakes, volcanoes, tsunamis, ice ages, all kinds of shit. At several times in the planet's history the majority of life has simply died off. For instance, at the end of the Permian era 90% of marine species and 70% of terrestrial species simply went extinct. At one point, an object the size of Mars collided with Earth and sent lots of material spewing into orbit around the planet (later coalescing into the Moon). And the world is still here. If anything is going to come and obliterate the planet entirely, it would have to be really freaking huge. And judging by the fact that nothing has done that in the past 4 billion years, it seems extremely unlikely that anything of that magnitude will happen in the few decades we have on this planet.

There is the slight possibility that some kind of mass extinction event could occur again, wiping out the human species. But again, no such mass extinction event has occurred since the dinosaurs died off 65 million years ago, so the likelihood of this happening within our lifetimes is again very minuscule. And even then, many mammal species were able to survive. If our primitive mammalian ancestors could find a way out of that, our species, with all its complex reasoning abilities and technological advances, would have a pretty good chance of surviving a disaster of that magnitude.

Our species is going to go extinct. This is undeniable, as all things in this universe are temporary. Nothing lasts forever. But I don't think we really have anything to worry about in our lifetimes, and the Earth as a planet probably won't end for at least the next 3 billion years, when the Andromeda Galaxy will collide with the Milky Way.