We know that Homo sapiens will not exist forever. Given this, how should our species end? What are the reasons, if any, to delay our extinction? In this paper, I show that the pre-eminent reasons which favour prolonging the existence of the species are partial: they will arise from the particular attachments and projects of the final few generations. While there may also be impartial reasons to prolong the species, these reasons are liable, with time, to reverse their valence: we (...) can be reasonably confident that they will ultimately recommend hastening the demise of the species. Consequently, it is likely that our descendants will eventually face a difficult -- possibly tragic -- conflict, between partial duties that recommend living on, and an impartial duty to extinguish the species. (shrink)