In "A Modest Proposal" why does the narrator express the hope that his plan will not be liable to the least objection just before he introduces it?
Even before the narrator expresses this hope, he begins to outline the importance of his plan as well as some of its intended benefits, though not the plan itself. He describes poor Irish mothers with their hungry children dressed "all in rags," and he expects agreement from "all parties" that this is a "deplorable" condition for the kingdom to be in. He believes he has found a solution that will make "these children sound and useful members of the commonwealth." The narrator's solution, he says, will "provide for them" so that they will no longer be a burden to their parents or the church and will not be forced to beg on the streets; in fact, they will help to feed and clothe others. His "scheme," he claims, will even curtail infanticide. The narrator does a little math to show just how many children end up in such a pitiable state as beggars and how much damage these children, grown into thieves without home or conscience, can cause.
So far, he has not actually mentioned the details of his proposal: that Irish families sell their babies as a food source to the English. He has vaguely alluded to one benefit of his plan––that the poor children will help to feed and clothe others––but he has not come to specifics. Finally, he says,
I shall now therefore humbly propose my own thoughts, which I hope will not be liable to the least objection.
Up till now, everything the narrator has said sounds perfectly reasonable; he seems to feel genuine care and concern for these piteous children, and he's already presented some of the potential benefits not only to the children and their families but also to the entire kingdom. How could anyone not be in favor of such a plan, whatever it is? By naming this hope, that no one will make even the smallest objection, the narrator continues to suggest that his proposal is a very "modest" one, something that is so reasonable that no reasonable person would take issue with it. Such an assertion has two purposes: the narrator himself, who believes in his idea whole-heartedly, implies that his proposal is so sound and rational that no rational person could object, and Swift continues to show us how absolutely ridiculous this narrator truly is. We are not meant to agree with this speaker; we are supposed to think he and his proposal are atrocious, as Swift does, and to experience moral outrage at his suggestion of cannibalism. Lines like this help to create the dramatic irony (where we, the audience, know more than the character Swift has created to narrate this text) that underpins the whole text and helps us to identify and understand its satire.
In Swift's "A Modest Proposal," when the speaker says that
I shall now therefore humbly propose my own thoughts, which I hope will not be liable to the least objection....
he, first of all, is literally saying that he hopes no one will object to his proposal. This makes sense because he is proposing something that he supposedly wants others to approve of. He would naturally want everyone to agree.
Figuratively, of course, the speaker is being ironic. He says he hopes no one will object, because he knows everyone will object. He uses this kind of irony throughout the essay, starting with the title: his proposal is anything but modest.
That's the long, official answer. The short answer is that he's being funny; making a joke.
In my opinion, the author puts this phrase in as a way of making his proposal even more satirical.
In this essay, one of the things that makes it so effective is how deadpan the author is through the whole thing. There is not really any place in the essay where he makes it look like he's joking. So he's very seriously putting forward this proposal that is just totally outrageous.
I think that the line you mention helps him do this. It's like he's starting out saying "this is totally serious, no one could possibly object to this."
So, I think he says it to make it sound like he's more serious so that his satire will be more effective.