The irony between conservative and progressive people
There are a litany of ironies in this book stemming just from conservative and progressive politics. Perhaps most notably, it is ironic that Kennedy praises one man for leaving a defunct political party (Adams), and also, he praises a man for staying in a broken political party. Ironically, Kennedy's views about justice are simultaneously compatible with any political belief system.
The irony of Houston's bravery
One of the aspects of bravery that Kennedy credits Houston for is Houston's silent acceptance of his role in the Confederacy. Kennedy says that when they try to give Houston a position of power, Houston declined, proving his loyalty to the original cause of the Union. Without a way to advocate that, he silently withdraws himself from power.
The irony of Taft's defense
Kennedy praises Robert Taft for his criticism of the Nuremberg Trials. Ironically, Taft's courage is offered in the defense of literal enemies, literal Nazis no less. The irony of defending Nazis is already way ironic, but it goes even further because Taft is technically correct, at least philosophically, because the Nuremberg Trials were literally done ex post facto as he argues.
The irony of groupthink
Kennedy's praise for these instances of courage is also a warning against the insidious nature of human groupthink. He calls on the reader (silently) to think for themselves! Although group identity is a surefire way of feeling safe and secure, Kennedy argues that true heroes are those who are waiting to see where their culture is incorrect, and to speak out in those moments of injustice.
The irony of public opinion
Because public opinion is often extremely polarized, the odds of offending someone go way up, especially when a person is disagreeing with not only their political opponents, but also their own political allies. Adams, Webster, Houston, Ross, Norris, and Taft all speak out in a way that costs them status in their own parties.