Kristi Noem, the South Dakota governor and Republican vice-presidential hopeful, on Sunday again defended killing a family dog and goat on her farm, two days after the Guardian revealed how she describes those actions in a forthcoming book.

“I can understand why some people are upset about a 20-year-old story of Cricket, one of the working dogs at our ranch, in my upcoming book – No Going Back,” Noem wrote on Twitter/X.

“The book is filled with many honest stories of my life, good and bad days, challenges, painful decisions, and lessons learned.”

Noem’s book comes out in May. The Guardian obtained a copy and reported how Noem recounts the story of Cricket – a 14-month-old, wire-haired pointer – ruining a pheasant hunt and killing a neighbour’s chickens.

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

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

The governor describes taking Cricket to a gravel pit and killing her – then deciding to mete out the same fate to the unruly, uncastrated goat. The second killing took two shots, says Noem, adding that when it was all over her daughter Kennedy came home from school and asked: “Hey, where’s Cricket?”

Kennedy Noem is now 27 years old, making her, by the governor’s statement, just seven at the time of her mother’s decision to shoot Cricket and the unnamed goat.

Amid widespread disbelief that a contender to be selected as Donald Trump’s running mate would commit such a tale to paper, many observers deemed Noem’s hopes of national office as dead as Cricket and the unnamed goat.

Noem defended her story on Friday, saying it demonstrated the harsh realities of rural life that only recently saw her family put down three horses too.

But animal rights groups condemned Noem.

“There’s no rational and plausible excuse for Noem shooting a juvenile dog for normal puppy-like behavior,” said a statement from Wayne Pacelle, president of Animal Wellness Action and the Center for a Humane Economy. “If she is unable to handle an animal, ask a family member or a neighbor to help. If training and socializing the dog doesn’t work, then give the dog to a more caring family or to a shelter for adoption.

“Raising and caring for a dog takes patience and kindness. Tens of millions of Americans who know and love dogs have to wonder about a person who expresses hatred for a young female dog and kills her.”

Meanwhile, one activist wrote to police Friday asking them “to ascertain whether all the legal and ethical guidelines were followed, given the high-profile nature of the incident”.

“Governor Kristi Noem … has publicly stated that she shot and killed her own dog,” said the missive that Chaz Stevens, the chief executive officer of ESADoggy, sent to police. “This incident raises significant concerns about animal welfare and the circumstances that led to such a drastic action.

In her Sunday post, Noem said: “What I learned from my years of public service, especially leading South Dakota through Covid, is people are looking for leaders who are authentic, willing to learn from the past, and don’t shy away from tough challenges.

“My hope is anyone reading this book will have an understanding that I always work to make the best decisions I can for the people in my life.

“The fact is, South Dakota law states that dogs who attack and kill livestock can be put down. Given that Cricket had shown aggressive behavior toward people by biting them, I decided what I did.”

According to the South Dakota legislature, livestock “means cattle, sheep, horses, mules, swine, goats, and buffalo”.

A spokesperson for Noem did not immediately respond to a request for comment about how chickens are not mentioned in the state’s definition of livestock.

The governor’s post Sunday did not mention her decision to kill the goat.

Ramon Antonio Vargas contributed reporting