It's not only a shaky metaphor from the sentimental aspect, it's a downright bad one from the economic point of view. Individual cattle are expensive, and as a result, it makes economic sense to invest in their care. Even a ruthless person would not let a sick cow go without having a professional take a look to see if there was a way to restore it to good condition, but heartless or broke people often do decline to pay for veterinary care for a pet.