Should cats be culled to stop extinctions?

[Spendulus]

Recently there's news that concerns some of the people around the internet so I though if it is worthy to open up a discussion and share anyones opinion about it.
According to the news

"Scientists are calling for a widespread cull of feral cats and dogs, pigs, goats, and rats and mice to save the endangered species they prey upon.

Their eradication on more than 100 islands could save some of the rarest animals on Earth, says an international team.

Islands have seen 75% of known bird, mammal, amphibian and reptile extinctions over the past 500 years.

Many of the losses are caused by animals introduced by humans.

Not naturally present on islands, they can threaten native wildlife."

https://www.bbc.com/news/science-environment-47721807
https://www.smh.com.au/national/war-on-feral-cats-australia-aims-to-cull-2-million-20170214-gucp4o.html

From what I believe culling the animals will drastically drop the chance of said species to go extinct but it raises a question if it is a moral thing to do.
Neutering the animals is also a good thing because it lowers the birthrate but they are still capable of hunting endangered species around the island.

well that depends on point of view, some people want to have a more "catish" world