Animal species come and go. It's not our doing - extinctions happened long before humans even existed. It's the way our planet works.
It may not always be our doing, but humans have a pretty good track record of wiping out animal populations. Wasn't the latest one the black rhino? Humans also cause extinction. It's not just a Mother Nature thing - we seem to have inherited the trait. I think it's plausible for humans to affect nature just as nature affects us.