How does the title of "a modest proposal” indicate that swift is writing a satire?

Swift, though in his title mentioned it as a modest proposal, but it is ostentatious and immodest proposal.

Explanation:

Satire is a rhetorical device used by the writers to expose and criticize the corruption prevailing in the society.

The full title of the essay is "A Modest Proposal For preventing the Children of Poor People From being a Burthen to Their Parents or Country, and For making them Beneficial to the Publick."

In his essay, Swift makes an appeal to the poor Irish parents to sell their infants as a food to the rich. In this manner, these children will not be a burden to their parents and will be beneficial. The readers are appalled by such an appeal or a "modest" proposal. But by saying this, Swift is drawing the readers attention to the ill-treatment of Irish by English, and in a satirical way appealing British Government to make some policies to help these Irish poor.

In this way, Swift indicated, by creating a contrast in his title and the content of his essay, that he is writing a satire.