When is species extermination a good thing? When the species is a deadly disease, say polio or smallpox. Getting rid of ebola or hantavirus would work, too.
In other words, when a species does its level best to exterminate humans, then it's okay for us to exterminate it. We've supposedly accomplished this with smallpox and are working on it with guinea worm.
We would do it with polio if al Qaeda crazies didn't get in the way. The polio deal is complicated by the fact that the CIA used faux polio vaccine teams to find Osama bin Laden. Good end, lousy means.
The Wall Street Journal has a Feb. 8, 2013 article about this topic, I provide no link as a subscription is required to see it.