While it is true that humanity is killing off species at an alarming rate, I don’t think this trend will continue indefinitely. The previous mass extinctions were driven (or at least initiated) for the most part by external events to the ecosystem, with reductions in the sustaining energy of the ecosystem and other consequences lasting for millions of years.
The rate at which we destroy ecosystems, on the other hand, is kept in check by our own population. Unless we pass some dire tipping point and cause the destruction to spiral out of our control, we will eventually hit a population limit, beyond which the planet can’t sustain us. It’s possible that we have already passed this limit; in that case, much like the current recession was caused because people borrowed money that didn’t actually exist and corrected by a return to the amount of real money left in the economy, the human population will be forced to decline, either through some sort of saturated-ecology problem (hunger is a big one; war could also be considered a limiting factor when resources become scarce) or simply through lower birth rates. Either way, the current mass extinction will not be as dire as the previous ones because, even at a faster rate of extinction, it will last for a much shorter period of time.
If I’m wrong and Earth becomes an ecumenopolis, it would instead bode well for humanity’s continuous expansion to other planets and we would nevertheless have the room to save what species remained extant.
…Barring a runaway process which takes matters entirely out of our hands. Watch those greenhouse gases!