The irony of survival and death
It's ironic that Gabriel's father starts the novel on an operating table, then gets better and looks like he's going to make it, and then dies. The irony of his death is that he probably thought that he wasn't going to die, but then again, the fear of death made him want to confide his secrets with someone. When he dies, he has already made peace in a way, because ironically, his survival showed him the truth about death—and therefore he told someone his secrets instead of taking them to the grave.
The irony of the review
For a father to review a son's book as being salacious and indulgent and downright offensive—that's deeply ironic, because to a child, a father's approval has something divine about it. If a father tells his child that he loves the child and that he's proud of them, that gives the child an advantage in life, because it truly does instill them with the confidence it takes to believe the best about themselves. Therefore, the father in this book is ironic, especially when he openly reviles his son's work to the entire community.
The irony of the involvement
Does it seem as though the father has a guilty conscience? Yes, and it only gets worse the more his journalist son goes snooping for the truth. Although he openly rejects and hates his son's work, there is an ironic twist: his father was more than complicit to the horrific mistreatment of Jews in the Holocaust. In fact, he was an informant to the government, a spy against his own people. That's why he doesn't like his son's appetite for honesty.
The irony of an honest affair
It's ironic and cheap to say, "I feel I can be honest with you," to a complete stranger. For one thing, the mistress knows the husband way less than a wife would, so perhaps a wife would be more suited for real honesty. But that's the irony. The father saying, "I'll be honest, but not with my family," is a little like saying, "I'll be honest, but not too honest." In other words, his perception of honesty is ironic because he doesn't feel it is dishonest to break his wedding vows.
The irony of the exposure
This man spent his whole life hiding a secret that he knew could destroy his legacy. His undeniable influence in the community and in the public mean that he has built his life as a glass house. In the end, he chooses to confide a secret in his mistress. Then he dies and she tells everyone what he said. This ironic moment when his legacy is tarnished by the very person he sought to be honest and open with—there's something poignant and fair about it.