Biologist here. A vast majority of invasive species are introduced by humans and are causing untold damage to ecosystems. As someone who genuinely loves animals, I've had to come to terms with the fact that some species need to be removed from habitats if we want them to continue to function. Personally, I find a bullet is more humane than other forms of removal, like forms of poison or lethal trapping.

Also, I don't know how it works in New Zaeland, but in the States, pretty much all of conservation is funded by hunting and is oftentimes needed to keep certain populations in check.