This study finds that Humans are bothered more by the prospect of losing 80% of the human population than by total human extinction:
Eastern philosophy/religion may have some wisdom to offer here, in that consciousness of reincarnation allows us to realize that attaining a human birth and thus human existence is a better option than incarnation as some other species with less capacity for moral reason and self-control.
If humans go extinct, or even if we just keep devolving into a more emotional-collectivist materialist (post)modern cultural/spiritual state, that would force us to reincarnate into many lifetimes of suffering before eventually progressing to a more peaceful civilized existence, if indeed we ever achieve that in the future.
Presumably if humans go extinct, some other species will evolve the capacity for moral reason and self-control that humans have, along with control of our environments, resources, etc.; but reaching that state requires going through many traumatic lessons and other growing pains.
It would be better to maintain the history of achievements and failures we have to build on as humans rather than wipe our slate clean and start over, so to speak. Maybe if religion wasn't eschewed by so many modern people, the story of Noah and the flood would remind us that doesn't intend for us to be destroyed as a species:
11 I establish my covenant with you: Never again will all life be destroyed by the waters of a flood; never again will there be a flood to destroy the earth.”
So we humans should honor all the challenges and lessons we've overcome so far in our evolution as a species and attempt to survive and refine ourselves further.
The purpose of life isn't just to be social and enjoy ourselves. It is to realize our ultimate potential for civilization. Allow ourselves to drive ourselves to extinction or some other degenerative state of existence would defy that purpose. We should know better than that by now.