How does Swift portray himself throughout "A Modest Proposal"? In what places does he reveal an egotistical persona?
First, we should begin noting that the narrator of "A Modest Proposal" is a fictional creation used to make a satiric point. This character is not meant to represent Swift himself, but rather a type of person that Swift despises.
The speaker's persona is one created to counter the accusation that people concerned with Irish poverty were merely being sentimental. In a sense, Swift is doing a reductio ad absurdum of the notion that moral questions should be decided independent of sentiment. Thus the persona Swift creates appears eminently rational, approaching the problem of starvation in Ireland simply as a logical, pragmatic technocrat.
For egotism, we should take into account that Swift himself was a priest who served as Dean of St. Patrick's Cathedral in Dublin. In the Gospel of John, Jesus commanded that the primary duty of the Apostles was to "feed my lambs/sheep". For Swift, not alleviating suffering and hunger goes against his religious beliefs. He would have seen his narrator's callous approach to treating the lives of others as like the sin of Lucifer, a sort of extreme arrogance that puts human reason and will above divine ordinance, following his own "devices and desires" rather than moral and religious duty, which is a sort of egotism that would be considered the sin of pride (one of the 7 deadly sins).
As the title of this essay suggests, the speaker of this treatise makes every effort to present himself as, above all, a reasonable and modest individual who diffidently makes his "modest proposal." This is of course part of Swift's irony, as his proposal is anything but modest, and the voice of the speaker in this essay heightens the irony when the proposal is finally made. Note how this is achieved through the following quotation:
I shall now therefore humbly propose my own thoughts, which I hope will not be liable to the least objection.
What makes the way in which his ideas are expressed even worse is the logic, hard work and thought that has evidently gone into them through his many calculations, and his attempt to work out how much food could be made from a child and how many children could be raised and what price children as a food source could be sold for. Swift, by presenting these arguments in above all else a reasonable voice, shows the danger of a system of thought which is divorced from feelings and morality and only sees humans as a saleable commodity.