In Jonathan Swift's a proposal for the use of Irish manufacture how is he being satirical?
I think the prior answer assumes you were asking a question about Swift's "A Modest Proposal." From your reference to Irish manufacture, I will assume you are asking about satire in Swift's "A Proposal for the Universal Use of Irish Manufacture," which was published in 1720.
Swift begins his satire in the first sentence of the "Proposal" by noting that
It is the peculiar Felicity and Prudence of the People in this Kingdom [that is, Ireland], that whatever Commodities, or Productions, lie under the greatest Discouragements from England, those are what they are sure to be most industrious in cultivating and spreading.
Because the Irish during this period had turned their farming land into sheep pastures and were producing vast amounts of wool, rather than using the land for agriculture, Swift is pointing out that the Irish are industriously producing goods that the English do not want. Wool was a staple commodity of England itself, and there was no possibility that the Irish were going to market their wool profitably to England.
In a comment reminiscent of the satire in "A Modest Proposal," Swift notes that he has heard of a
. . . Projection Afoot for transporting our best . . . Straw . . . to Dunstable [a town in England famous for its straw hats]; and obliging us by a Law, to take off yearly so many Tun of Straw-Hats, for the Use of our Women; which will be a great Encouragement to the Manufacture of that industrious Town.
In other words, a proposal exists to send Irish straw to England where it will be woven into hats that are then sold to the Irish. Swift is attempting, through satire, to make the Irish understand the stupidity of sending their raw materials to England for manufacturing into usable products that are then sold to Irish. As he argues throughout this proposal, the Irish need to produce marketable goods with their own raw materials. Throughout the period in which this proposal, as well as "A Modest Proposal" was written, Swift was increasingly frustrated by Ireland's ignorance of modern (for the 18thC, that is) mercantilism.
In one of his most biting satiric statements, Swift comments that
. . . Slaves have a natural Disposition to be Tyrants: and that when my Betters give me a Kick, I am apt to revenge it with six upon my footman: although he may be an honest and diligent Fellow.
Swift is making a statement about how the Irish deal with the, oppression of England. Instead of fighting the oppressor (England), the Irish simply turn around and attack themselves, thereby assuring that the source of the oppression is never dealt with.
Swift's "A Modest Proposal" is considered one of the greatest satirical essays of all time and he has a number of characteristics that make it so effective.
One of the first is his very formal tone. Throughout the entire essay Swift maintains this tone as though he were addressing a session of parliament. Never once does he crack as he makes a proposal that is far from modest and more likely one of the most horrible ever made. But the tone is vital as he goes on at great length and in very specific detail about how the Irish children might be sold to their landlords.
One of the other important elements in his satirical treatment is the way that it mirrored some of the popular view of the Irish within the UK at the time. There was a general sense of indifference to the horrible famine that developed in Ireland at the time. By suggesting this horrific idea in such an even-handed and knowledgeable and confident tone, Swift succeeds in satirizing the inhuman attitude many of the British had towards the death and disease that was wiping out thousands upon thousands of their neighbors in Ireland.