The current rate of extinction is between 100 and 1,000 times higher than the pre-human background rate of extinction. What we're going through will be an extinction event on a timescale and severity that will be closer to the Permian or Cretaceous extinction, which resulted in the species death of 95% and 78% respectively, and caused by apocalyptic scenarios; meteors and volcanos effectively suffocating the planet. Never before has a single species been responsible for such destruction on Earth.
I suspect humanity will survive whatever future is yet to come. I just hope we managed to preserve a substantial percentage of natural diversity through that process.