Why do conservationists in Australia support the policy of killing cats?

In July 2015, the Australian government announced a "war on feral cats" with the intention of killing over two million felines by 2020. The threat abatement plan to enforce this policy includes a mix of shooting, trapping and a reputedly "humane" poison.
        Some conservationists in Australia are hailing this as an important step toward the rewilding of Australia’s outback, or the idea of restoring the continent’s biodiversity to its state prior to European contact. Momentum has also been building in the United States for similar action to protect many animals outdoor cats kill every year.
        In opposition are animal advocates including the British singer Morrissey who are appalled at the rhetoric of a war on cats and promote nonlethal methods of controlling the negative effects of cats as being more effective and humane.
        From a scientific perspective, there is little doubt that under particular geographic and ecological conditions, outdoor cats can threaten native species. This is especially true on oceanic islands whose wildlife evolved without cats and are consequently unadapted to feline predators. For example, when cats were introduced to Pacific islands by European colonists, their numbers grew until they frequently posed a threat to native wildlife.
        Some conservationists claim that cats are the single largest threat to biodiversity regardless of ecological context. One oft-cited study in Nature Communications claims that 1.4 to 3.7 billion birds and 6.9 to 20.7 billion small mammals are killed by cats every year in the United States alone. Yet some have pointed out that the scientific case for this claim is shaky at best.
        Why? Virtually every study of outdoor cats assumes that because cats in some habitats threaten biodiversity, they are a threat across all habitats everywhere. This is a projection from a small set of localized case studies to the world at large. In other words, a guesstimate.