Kristi Noem, the governor of South Dakota whose chance of being Donald Trump’s presidential running mate was widely deemed over after she published a description of shooting dead a dog and a goat, claimed reports of the story were “fake news” but also that the dog in question, Cricket, a 14-month-old wirehaired pointer, was “extremely dangerous” and deserved her fate.

“You know how the fake news works,” Noem told Fox News. “They leave out some or most of the facts of a story, they put the worst spin on it. And that’s what’s happened in this case.

“I hope people really do buy this book and they find out the truth of the story because the truth of the story is that this was a working dog and it was not a puppy. It was a dog that was extremely dangerous.”

The Guardian first reported Noem’s story of killing Cricket the dog and an unnamed, un-castrated male goat. The story is contained in Noem’s book, No Going Back: The Truth on What’s Wrong With Politics and How We Move America Forward, which will be published next week. The Guardian obtained a copy.

In the book, Noem says her description of killing a dog and a goat illustrates her willingness to do anything “difficult, messy and ugly” in politics as well as on her South Dakota farm – a defence she repeated before her Fox News interview.

Noem says Cricket ruined a pheasant hunt then killed a neighbour’s chickens, all the while presenting “the picture of pure joy”.

“I hated that dog,” Noem writes, adding that Cricket tried to bite her and proved herself “untrainable … dangerous to anyone she came in contact with” and “less than worthless … as a hunting dog”.

“At that moment,” Noem says, “I realised I had to put her down.”

Noem describes killing Cricket in a gravel pit, then deciding to do the same to the goat because it was “nasty and mean”, smelled “disgusting, musky, rancid”, and “loved to chase” Noem’s children, knocking them down and spoiling their clothes.

It took two shots – separated by a walk back to her truck to fetch more shotgun shells – to kill the goat, Noem writes.

Speaking to Fox News, Noem did not mention the goat.

Of Cricket the dog, she said: “It had come to us from a family who had found her way too aggressive. We were her second chance and the day she was put down was a day that she massacred livestock that were part of our neighbours. She attacked me and it was a hard decision.”

Repeating her claim that the story illustrated her willingness to make tough decisions, Noem claimed to have done the same through the Covid pandemic by “keeping my state open”, a stance she said invited media attacks.

Figures from the US Centers for Disease Control and Prevention do show South Dakota with a relatively low Covid death rate, with 71.2 deaths per 100,000 people, for a total of 776.

Noem’s Fox News host, Sean Hannity, tried to compare the governor’s decision to shoot Cricket with the case of Commander, a german shepherd owned by Joe Biden who was sent away from the White House – not shot – after being found to have been involved in more than 20 incidents of biting.

Hannity then asked: “You say here you said you follow the law in your book. What is the law?”

Noem said: “Virtually every state has a law in place that says the animals that attack and kill livestock can be put down in situations like this.”

A Guardian review of South Dakota state law found that Noem could have committed a misdemeanour, both by failing to control Cricket when she attacked and killed a neighbour’s chickens and by killing the dog later, on her own property.

A spokesperson for Noem did not respond to a request for comment on that point.

Noem continued: “Farmers and ranchers, they expect it. They know that once an animal like this starts killing and starts killing just because they enjoy it, that is a very dangerous animal. And that was the situation that we were dealing with.

“And I’m a dog lover. I’ve trained dogs for years, I’ve been around hundreds of them, of course. And so this was a tough situation and very difficult. But that’s what happens in rural America many times.”

Noem has also discussed a recent decision on her farm to put down three elderly horses – Lucy, Dunny and Tibbs – sharing pictures of the process including a horse standing in a freshly dug pit.

“These weren’t just horses,” Noem told Newsmax in March. “These were family members … they raised my girls.”

On Fox News on Wednesday, she said: “I hope people do read the facts of the story [about Cricket and the goat] and truly understand that I’m a mom, and at the time I had small children and a lot of small kiddos that worked around our business and people and I wanted to make sure that they were safe and that dogs that have this kind of a problem that have been to training for months and still kill for fun, they are extremely dangerous and a responsible owner does what they need to do and what the law will allow.”

On the page, Noem’s story of the day she shot Cricket the dog and the unnamed goat – titled “Bad Day to be a Goat” – features the arrival of a school bus and the emergence of her daughter, Kennedy, who by the governor’s own accounting would then have been about seven years old.

“Kennedy looked around confused,” Noem writes, “and asked, ‘Hey, where’s Cricket?’”