Why is it ironic that the pardoner preaches a story with this particular moral?
Chaucer was a genius of irony. He frequently exposes hypocrisy among all of his characters, especially those in the clergy. "The Pardoner's Tale" is perhaps the most extreme example in the book. For a little historical context, in Chaucer's day it was a relatively common practice for the church to sell forgiveness, or pardons. The Pardoner makes this even more sinister by openly admitting that he is fraud. He in fact has no authority to sell pardons.
The story tells of a group of people on a quest after Death. They aim to defeat this evil, but out of greed all plot to kill and betray one another for gold that they have found. One member of the party goes to get wine and food while the others stay behind. The group that stays plot to kill the other for his share; the one that leaves plans to poison the others. After the larger group betrays and murders their companion, they consume the poisoned wine and die as well.
The basic irony is simple: a man of lies and greed is preaching against lies and greed. The pardoner is abusing the principle of the story to serve a selfish purpose. What is more interesting, however, is how Chaucer opens this up to raise even larger questions. Aren't all people, after all, imperfect; and so isn't the practice of all pardons in some way corrupt? All moral services are performed to some extent by immoral people. Additionally, if the party is genuinely moved by the story, does the greed of the teller really affect the outcome? How important is the character of the storyteller in a moral parable?
It's ironic that the Pardoner preaches a story with this moral because he admits in his prologue that he essentially swindles people for money as his primary occupation. This is ironic because he admits this fact about himself, but the moral of the story he tells is essentially that greed can lead to death: he begins his tale by saying "But let me briefly make my purpose plain; I preach for nothing but for greed of gain." He goes on to say that he would take money from a poor village widow with hungry children so that he can keep "a jolly wench in every town." He is admitting to his hard-hearted ways, but then continues to tell his tale that illustrates the terrible repercussions that can occur when one is motivated simply by greed. It's terribly hypocritical, but is it possible that this is Chaucer's intent? It's possible that Chaucer may be bringing to light the motives of some men of the church who claim to be good and honest men. Regardless, the Pardoner is an example of a man who literally does not "practice what he preaches."
The irony of the Pardoner's tale is that he preaches on the very sin he commits. The Pardoner's prologue tells that he tries to pass off pig's bones as relics of saints, a pillow case as a shawl worn by Mary, etc. He decieves people trying to buy pardons from their sins by selling false pardons to earn himself money. This is greedy, as he takes advantage of religion for his own monetary gain.
The irony is that the Pardoner's tale is all about how greed is the root of evil. In the story, all the men die because of their greed and selfishness. Following his tale, the Pardoner asks the other pilgrims and on-lookers to give freely and buy pardons, encouraging them not to be greedy while feeding his own greed.