If extinctions are events, they are so only in geological time, and geological time is rather vast. The late Devonian extinction event, for example, was really a series of extinction pulses, spread out over 20-25 million years. Anatomically modern humans have been here for 200,000 years, tops. It would be a bit of an ask to expect us to have orchestrated something like that in the time available to us.
In terms of the percentage of species rendered extinct, we are nowhere near the levels of the five great extinctions. But the rate of extinctions we are currently witnessing may be far worse than at least some of these.
If there is a mass extinction event occurring today, we are not entering into it. We are already in it and have been for quite some time.
What we see today are simply segments of the same phenomenon. This is a pulsing wave of extinctions brought about, to a considerable extent, by humans: a wave whose nascent beginnings can be traced back 130,000 years. The late Quaternary extinction ‘event’ of 9,000 to 13,000 years ago: that was on us. The wave has become much bigger in recent years. But humans are walking, talking extinction events. The habitual extinguishing of other species is one of our defining traits.