It's important to differentiate between the speaker (the narrator) of "A Modest Proposal" and Jonathan Swift, the author of the piece. The speaker, an individual focused solely on economics, spends the first paragraphs of the essay expressing in moving terms the plight of the many poor people in Ireland: the women in rags begging with their children clinging to them, the young men who are so hungry they die when they finally do get a job from the exertion of the work, the people who sell themselves into slavery in Barbados because the alternative is starvation. After having articulated their plight, the narrator then unveils his "modest" proposal: that poor women fatten their babies for a year and then sell them as a gourmet delicacy for rich people's tables. The narrator goes on to describe all the benefits that would accrue from this sale of babies, benefits that further outline the miserable conditions in which the poor currently live--men would be less likely to abuse their wives if the women were carrying or feeding a salable commodity, women would be less likely to abort their babies, Ireland's trade balance would improve, and the poor would have money. The narrator even proposes hunts for poor children at about age 12.
Swift's purpose in writing this satire was to shock people into considering more humane solutions than cannibalism to the problem of Irish poverty--solutions he had proposed to deaf ears numerous times. The essay did succeed in shocking people and has remained a classic example of satire ever since.