how does swift tend to lend legitimacy to his proposal?

Swift's proposal is a satire, there can be no legitimacy in "eating" children. Swift's intent is to make people see other choices by using sarcasm and humor. Swift finally gets down to some real arguments when the narrator lists all the arguments that he will not give any time to. If eating the children were off the table, the people would have to turn to realistic arguments like these, such as the encouragement of virtue and thrift.