Sometimes animals on the farm have to be put down; reluctantly. It is a dirty job.
I have never known of anyone to put down a pet, or a working dog, and then publish the fact in an attempt to build a case they should be elected to higher office.
She didn’t think this through and raises questions about how much she actually thinks.
She thought the story as already out there, and her opponents would have leaked it anyway as an October surprise.
I completely agree with your take. On the farm my father had a rule that if any animal continually showed aggressive tendencies such that it put people (most important) or other animals or livestock at risk - they were put down. He had a dog that was wonderful around immediate family members, but it wouldn’t stop killing chickens and ducks and would be suddenly aggressive with visitors. It pained him to put the dog down but he didn’t hesitate. Then again, he didn’t go off and write a book about it either. The shoot, shovel and shut up rule tends to be part of the farmer / rancher way in my experience at least.