The baby in "Popular Mechanics" could be said to represent the sense of dignity that most of us have, a sense of self-worth. Both the unnamed man and woman in the story instinctively acknowledge that the baby is an intrinsic part of their self-worth and dignity. That's why they're so desperate to hang on to the child—quite literally. Their sense of self is so closely bound up with the baby that neither is prepared to back down in the violent, intensely physical struggle that follows, even if the baby gets caught up in the middle.
The supreme irony of his conflict is that neither the man nor the woman behave in a way that is consistent with their sense of self-worth. An insistence on one's dignity being respected has never looked quite so undignified. In their unseemly squabble, the warring couple act like little children, which merely adds to the sense of irony.
Each one believes that they are the right parent to take care of the child, yet both show a total inability to conduct themselves like the responsible adults they're supposed to be. Indeed, their conduct is so utterly reckless and appalling that it's likely that it leads to the baby's death.