The key to answering this question lies in the one-sentence paragraph that serves as the transition between the introduction of the proposal and the actual proposal. Swift concisely states:
I shall now therefore humbly propose my own thoughts, which I hope will not be liable to the least objection.
Swift skillfully lays out valid arguments to help the Irish people with poverty and overpopulation. Everything makes complete sense the way he spells it out. It sounds reasonable for him to say,
That the remaining hundred thousand [children] may, at a year old, be offered in the sale to the persons of quality and fortune through the kingdom; always advising the mother to let them suck plentifully in the last month, so as to render them plump and fat for a good table. A child will make two dishes at an entertainment for friends; and when the family dines alone, the fore or hind quarter will make a reasonable dish, and seasoned with a little pepper or salt will be very good boiled on the fourth day, especially in winter.
The irony comes in the fact that he's talking about eating children. If the reader puts aside his or her feelings, Swift's arguments sound pretty good. However, that is impossible to do, and Swift knows it. There is nothing "modest" about Swift's proposal. Swift was trying to get the English and the Irish to listen to him. By modestly proposing to use babies as a source of food and income, he was finally able to get some attention!