I think you're missing a valid distinction in types of extinction. Historical extinctions occuring through events such as sudden climate change or disease opened up new ecological niches which new species could expand into.
Man-made extinctions don't, in most cases. Where extinctions come about because of habitat destruction or dumping massive amounts of pollution into the habitat, ecological niches are destroyed instead of being recycled.
Another very common cause of manmade extinction is the expansion of species into new environments. This is especially common on islands, where species that evolve to fit the particular closed ecosystem in place get overwhelmed when human-introduced species and activities drastically change the ecosystem. Again, there are no real new niches created or, if there are, they are niches for animals like rats, dogs, and pigs which follow human activity and are hardly scarce to begin with.
The effect in each case isn't merely change from one species to another, but a net loss in biological diversity.
I'm not sure that the distinction you're making is one that can be made, because you have to infer tha mankind is unnatural, whereas I'm assuming that anything mankind does is as natural as, say, an extraterrestrial event like a meteor landing off the Yucatan penninsula and causing a massive extinction.
Human activity is pumping a great deal of carbon into the atmosphere through the burning of fossile fuels -- I seem to recall from my geology class that the earth's atmosphere contained far more carbon in the precambrian and cambrian periods than it does now.
I suppose you could argue that humans have choices about these things, although I'm not sure that we do in any real sense. Yes, you can forgo a bag of potato chips because you'll be sitting down to a steak dinner in an hour, but I doubt that, absent the sort of coercive force associated with totalitarian regimes, you could convince people to starve themselves for their own good -- or go cold or forgo fresh fruit in the winter or deny themselves any of the other benefits that our energy economy make affordable.
I have no problem with preserving habitats or species, and I'm happy to do it, but I also concede that it's a choice I'm making on the basis of a rather stultifying dogma, one which puts rather a low value on human happiness and progress.