"A Modest Proposal" is a satirical essay that suggests that poor Irish families should sell their children as food. While this is clearly a ridiculous idea, the author, Swift, is in fact making a social commentary; he is remarking upon the heartlessness of those who do not seem to see or care about the plight of the poor, and suggesting that their attitudes or the usefulness of their efforts might as well result in a suggestion like his own.
Satire of this nature is a way of framing your opponent in an over-the-top, ridiculous manner, and then criticizing them for it. This is also called a "strawman" or "ad-hominem" in the context of debate, as it suggests a slightly underhanded, vicious means of taking your opponent's position and making it seem much worse than it actually is, to the point that no reasonable person would agree with it. No one was actually suggesting that the Irish sell their children, but this form of satire serves to frame Swift's targets as uncaring, inhumanly selfish elitists, unconcerned with human rights or emotions.
The agreement takes place in the second paragraph;
I think it is agreed by all parties that this prodigious number of children in the arms, or on the backs, or at the heels of their mothers, and frequently of their fathers, is in the present deplorable state of the kingdom a very great additional grievance; and, therefore, whoever could find out a fair, cheap, and easy method of making these children sound, useful members of the commonwealth, would deserve so well of the public as to have his statue set up for a preserver of the nation.
This actually seems like a very reasonable statement. Swift is basically saying, "I think we can all agree that, conditions being as poor as they are in Ireland, the great number of children puts an additional strain on everyone. If there was any way of turning these children from a resource-draining problem into a helpful contribution to society, I think the person who figures out how to do it would be thanked for doing so."
Swift's intent is to bring us onto his side; to make us agree with his train of thought and be led that much more shockingly into his revelation of his real idea. He's appealing to common sense and reason, in just the same way that the title, "A Modest Proposal", implies that this is merely a humble sorting-out of a problem like any other. By doing this, Swift elicits a stronger reaction than he would have garnered otherwise; had he begun simply by stating "The poor should sell their children as food!" there would be no reason to read further; we would write him off as a crazy person, we would not recognize that this piece is satire, and we would not continue to read it.
Swift's agreement serves both to enhance the emotional and literary impact of his "idea", as well as to ease us into the piece by disguising it as a reasonable, well-written argument. Satire does, of course, require that the reader recognize the inherent insanity of the satirical statement, rather than taking it seriously; by juxtaposing satire with what seems like a reasonable statement, we recognize a jarring shift in tone, and hopefully, the fact that this shift is so large that it indicates satire.