To be fair not every other species, life will carry on just fine once we're gone, new species will evolve to fill the niches left empty by the species we killed off. Just give it a few million years.
The devastation we bring upon the planet will be disastrous in the short term (planet time scale), but it’s just a new set of living conditions for evolution to bump up against. Us humans and many other species decently high up the food chain will suffer greatly, but I have no question that life will continue. There’s radiotrophic fungi growing in the Chernobyl containment. Life will find a way. Humans - we’ll see.
Maybe, we don't know what climate change has in store for us. The most extreme scenarios in models are starting to play out right now, and we're only at the beginning of what's projected to occur.