An old newspaper aphorism has it that it is only news when a man bites dog, not when a dog bites a man.

However, there are exceptions.

And one of them concerns conservative Republican Gov. Kristi Noem of South Dakota, who recently saw her vice-presidential dreams explode.

It happened after it was revealed that she shot her “untrainable” and “aggressive” hunting dog Cricket, a 14-month-old wirehaired pointer.

She shot him in a gravel pit after Cricket failed as a hunting dog, even though the dog had “the time of her life” chasing birds. The dog then attacked and killed a neighbor’s chickens.

Apparently, there are no veterinarians in South Dakota to euthanize dogs.

Now, the dead dog has come back to bite Noem, so to speak.

Noem blew her chances of becoming Donald Trump’s running mate so badly that Cricket would stand a better chance.

In an apparent attempt to show the world — and Trump — that she could make tough decisions, Noem wrote about it in her just-released book with the overlong title, “No Going Back: The Truth on What’s Wrong with Politics and How We Move America Forward.”

Noem may not be going back, but she certainly is not going forward, not after writing about shooting Cricket and then shooting a “nasty and mean” goat in the same gravel pit, as well as several horses that had to be put down on her family farm.

In fact, after dragging the goat to the gravel pit, she had to shoot it twice after the goat survived the first round.

Trump, who has enough baggage of his own, certainly does not need any more, like having dog lovers and animal rights groups breathing down his neck.

You can just imagine, with Noem at his side, Trump hating reporters from the networks asking,” Mr. Trump, when is the last time you shot a dog?”

It is one thing to sadly put a sick dog to sleep. It is totally something else to shoot a healthy dog because Noem could not train the dog to hunt pheasants and then write about it as though it were some noteworthy accomplishment.

Politicians are supposed to love dogs or pretend that they do. They do not shoot them and then write about it.

What was she thinking?

She said, “The reason it’s in the book is that the book is filled with tough, challenging decisions I’ve had to make throughout my life.”

She cited South Dakota law that she said states that dogs that kill livestock can be put down. “It was not a pleasant job, but it had to be done,” she said.

One fellow Republican who was quick to criticize her was former Massachusetts Gov. Mitt Romney, who had his own canine problems when he ran for president against Barack Obama in 2012.

Back then, Romney was dogged by the pro-Obama left wing media for allowing that he once drove his family on vacation in 1983 with his Irish Setter, Seamus, on top of the car in a windshield-equipped carrier.

When the dog had bowel issues atop the car, Romney stopped at a gas station, washed the dog, the carrier and the car before moving on.

While the liberal media mocked Romney and accused him of animal cruelty, reporters sympathetic to Obama made little of the fact that Obama, living in Indonesia as a child, used to eat dogs.

“I was introduced to dog meat (tough), snake meat (tougher), and roasted grasshopper (crunchy), he wrote in his book “Dreams from My Father.”

All of which stirred Romney, who is not seeking reelection as a U.S. senator from Utah, to comment: “I didn’t eat my dog. I didn’t shoot my dog. I loved my dog, and my dog loved me.”

Politics has gone to the dogs.

Peter Lucas is a veteran political reporter. Email him at: peter.lucas@bostonherald.com