First, and this is important, it is not "Swift's" plan that we are discussing, but that of his clueless narrator. Swift does not approve of this proposal and wants his readers to be horrified by it. Only the narrator, who is not Swift, thinks it is a good idea.
It is not until the ninth paragraph of this essay that we come to understand that the narrator is proposing that the poor sell their babies for food. It is here that he says he has learned from an "American" that
a young healthy child well nursed is at a year old a most delicious, nourishing, and wholesome food, whether stewed, roasted, baked, or boiled; and I make no doubt that it will equally serve in a fricassee or a ragout.
This is a shocking and nauseating proposal, and yet, although the narrator is clueless about the boundaries of common humanity, he is a good rhetorician. He does his best in the opening paragraphs to first use pathos—appeals to our emotions—and logos—appeals our logical, rational minds—to build support for the idea that the situation of the poor is urgent. He begins by painting a heartbreaking picture of a poor woman in rags trailed by her starving children and then convincingly shows that he has a grasp on the statistics about the number of poor and their prospects. This builds his credibility, and by the ninth paragraph, we are anxious to hear his proposal. The trouble is that it is heartless and barbaric.