At this moment, we are undergoing a massive loss of species on par with the six great extinctions of history such as the most recent one 65 million years ago and the Great Dying of 250 million years ago. Being a good existentialist, I agree that we should do all we can to prevent loss of biodiversity even if the effort is likely to be futile. However, a part of me is secure that life will go on regardless of what happens now. Each great extinction is always followed by a flowering of new life. It was only because of the demise of the dinosaurs were mammals able to rise. I agree that it is a major cause of concern as to whether we will survive this extinction but on the long time scale all species eventually go extinct.
Ironically, one reason for my optimism is the large amount of garbage we dump into the environment. The toxicity of a waste product implies that it is bioreactive and hence could be exploited. Remember that oxygen was once an environmental toxin that forced major changes to life on earth. The extra methane and carbon dioxide we currently spew into the atmosphere could likewise be utilized. I'm sure new species of life will be found in garbage dumps sometime in the future.
There are already some signs of adaptation to the modern world even by large animals. For example, deer are now doing so well in cities and suburbs that some communities need to cull them. New York City has several pairs of thriving peregrine falcons. Some fear that beautiful species like orchids, parrots, and sea otters will disappear leaving behind only drab scavengers like cockroaches, coyotes, crows and rats. I think we need to give life more credit. I don't think beauty is necessarily correlated with fragility. Also, our standards of beauty have been shaped by our environment. As the environment changes, so too will our brains and hence what we consider beautiful. Barring a catastrophic event like a nearby supernova or a complete loss of atmosphere, I think we can be fairly certain that life will continue to flourish on earth in spite of what we do.