The main irony in the story is that both the man and the woman want the baby but in the end neither get what they want. Initially, the man just wanted a photo of the baby, but the woman wouldn't even allow him that. So he gets up to leave and tries to take the baby with him, but the woman refuses.
Soon, the members of the unnamed couple are embroiled in a fight, with each one pulling at the baby. It isn't very long before the fight gets physical, with a flowerpot being knocked over in the ensuing melee. Both the man and the woman are determined to have the baby, and are prepared to do whatever it takes to ensure that they will prevail in this increasingly titanic struggle.
A further irony, and a rather chilling one, at that, comes near the end of the story, when we're told that the matter has been "decided". Only it hasn't, at least not in the way that either the man or the woman originally intended. They both wanted the child, and yet neither has what they wanted. This is because the child, it is strongly suggested, is dead, killed in the midst of the epic physical struggle between the warring couple.