If you graph human existence, the amount of people increases towards the end of the graph. The end of course represents the end of the human race.
When you (yes you!) were born there was a higher probability that your location in humanity's timeline is closer to the end as opposed to the beginning simply because our race undergoes geometric growth.
Based on this logic (as well as taking a few subtle assumptions involving probability mechanics) we can come to the conclusion that our race is much closer to it's extinction rather than birth.
This argument has been under constant debate since it was first proposed by Brandon Carter.