The irony of Christopher Columbus
Columbus is an ironic character in this book, because he represents something so cherished in American history, but he turns out to be something of a villain. It seems from his journals that he knew much about the intentional removal of Native Americans. He knew about much of the violence against children and women, because he writes about it in his journal—not exactly a picture of ethical virtue.
The irony of WWII and the bombs
The historical debate about the use of nuclear bombs has been heated, but in America, the historical concensus seems to be that the use of the bombs in Nagasaki and Hiroshima were politically necessary because they were the only way of ensuring the end of the war, but actually, what it did was it introduced a new, unbelievably worse form of warfare—the elimination of entire cities with the use of nuclear bombs. And Zinn proves that it was not necessary—he paints a picture that makes it seem that the true reason the US used the bomb was as a threat to the rest of the world that America was not to be messed with.
The irony of Vietnam
The irony of Vietnam has been discussed ad nauseam, but essentially, there are two main ironies: That the people largely opposed the war, and that the war didn't seem to involve America in any way, except that the Vietnamese were interested in establishing a Communist government. In other words, it was Capitalism at war with Communism—but real people died, even though back home, most people wouldn't even agree that Capitalism was necessarily a perfect economy.
The ironic presence of anarchism and socialism
Anarchism and socialism are sometimes thought of as modern movements, but Zinn traces their origins back for a lot longer than that, since the Colonial era at least. They are often thought of as 'political outcasts,' but that simply indicates that the majority is setting the tone in public perception. The irony is that the competitors are all regarded as evil, simply for being less capitalistic, in this case.
The irony of the "War on Terrorism"
The War on Terrorism is terrifying itself, which is logically contradictory, Zinn argues. The horror of those decisions were that the government used fear mongering and propaganda to shape a public opinion that allowed very wealthy people to meddle abroad in serious ways. Zinn shows three main involvements—in Iraq, in Palestine, and in Saudi Arabia.