Okay, this might be a bit meandering stream of consciousness...
Feeling bad because entire species go extinct due to our own behavior is an uniquely human experience. It's not something that exists outside of our own human awareness in the broader world.
When the last butterfly goes, it's not aware that it was the last of it's kind. It's not even aware of the complexities that caused it and it's kind to vanish. It simply dies. End of story.
Now, that butterfly is a part of the Universe. This big thing that just "is", where basic laws of entropy and quantum physics just run their course, unattended, until trillions upon trillions of years from now, all that is left are subatomic particles randomly appearing and disappearing as the last black hole finally evaporates.
There's a paradox at the heart of our human condition. Our awareness has brought us to the apex of the food chain. We are seemingly in control of how we shape the conditions for our own survival. But that sense of rational control is just the veneer on top of behavior, feelings, urges and instincts that we share with other species.
We can imagine how we can reach for the stars, go to other planets and build great machines to do it. We have created morals, ethics, science, religion, nations, lore and legends to put ourselves at the center of things. But there's a dissonance we can never hope to overcome at the heart of our experience: We are not really in control. And that word "control" is just a mental construct that helps us make sense of the world around us.
Whatever you and I, living people, do or do not do, small or big, has an impact. No more, no less. We can't avoid not throwing stones in the pond and causing ripples. Trying to preserve Earth as it exists today, either through technology or through profound policy changes is just as futile is holding your breathe. Our mere existence predicates change, willing or not.
The idea that humanity shouldn't exist is just as futile. Remember, the Universe just "is". It does not care about our existence. And that butterfly doesn't care whether humanity is around or not. The only ones who agonize over the morality of existence are... humans. That's the price we pay for having evolved an acute sense of awareness of the past, present, future and the world around us.
Even though we are in this extinction event, life will still be around long after we are gone. Bacteria sprung into existence even long before Earth's atmosphere contained 21% of oxygen. If we could travel back in time, Earth would be a very alien place to us. And it will be a very alien place once again eons down the line. Maybe it will be just fungi and algae, maybe it will be dense forests of plants and animal life that are nothing like what we know today.
There are more galaxies then there are grains of sands of all beaches on Earth. Even if Earth becomes a barren rock, probability has it that the Universe might be teeming with life. Just at this point, right here, right now, in this corner of the Universe, humans are the only ones agonizing over that question: Are we really alone in our bubble of awareness? Or are there other species who feel and experience what we feel experience? And the vastness of things will never allow us to solve that question, unless by random chance.
None of that is by any means an excuse to sit back and just take the ride. The very paradox that is our human awareness forces us to make decisions that will have an impact, that will cause suffering at one point or another. Either by giving up on consumerism, or by grieving over the loss of biodiversity.
But when we do feel that creeping sense of depression over what we are losing, it's good to remind ourselves that the stories we tell ourselves - including climate change and mass extinctions - hide a far larger, incomprehensible reality in which mental constructs don't carry any particular larger Meaning our morality.
We only control so much after all, it's entirely up to us to define how far we are willing to go to find out to what extent, and what we, humans, are willing to accept as a consequence. Accepting that nothing will ever stay the same anyhow, not even life, humanity, culture or civilization as we know it today on this planet, can help us to find a measure of some comfort and re-frame that journey a bit.