As in there’s nothing morally right or wrong with it.
There are hundreds of animal species that we eradicated by complete accident (Rocky Mountain Locusts)
There are also hundreds of animal species that we eradicated on purpose or out of greed (screwworm, passenger pigeons, etc.)
There are also hundreds of species we have been trying to eradicate for centuries and yet they still persist (cockroaches, flies, etc.)
I say this on the premise of “humans are a part of nature” because well… they are. They live on planet earth, and they adhere to its rules like every other animal.