The irony of childhood
Childhood has innocence as its irony. That is dramatic because the child is aware that they do not know everything, but they don't know what they don't know. That irony blooms in this memoir as Balakian details the process of gradually learning about his ethnic heritage and his family's status as refugees. That bloom could be described as ironic because the writer and reader each understand that this memoir concerns a deep passion that Balakian does not know about in the memoir's narrative scope—at least at first. In other words, the book is largely a book about how he gradually learned the facts that sent him into a life of research and thought so he could publish said book.
The grandmother's truth
The irony of Balakian's grandmother is that she is a grandmother to him, meaning that she appears as a sweet lady with funny stories and good advice who often cooks amazing food, but that is just what she is to him specifically. Without reference to her role as grandmother, what is Nafina's life really like? She survived one of the most tragic and devastating events in European history and lived to tell about it, but then chose not to tell about it. This means that her account is withheld from him by dramatic irony.
The rejection of family
Ironically, this author seeks to serve his family by recording their history, but they reject him again and again. They are happy to share stories, but they will not be interviewed. This is because they choose the content in their stories, but memoir involves the revealing of deeper truths. The family rejects his efforts and some people try to convince him to drop it and let the family move on in peace. This irony points to the reason why the work is valuable: we cannot afford to ignore events like the Armenian Genocide, and that is an event which was neglected by the public at the time.
The fragmentary nature of truth
In Balakian's story, the truth is something that is rarely attained. This is true from his literal experience because his family is shy to share about the genocide on account of personal trauma, but it is also true in a more abstract way. The truth itself is shown to be fractured, and it is the job of this memoirist to re-establish the portrait that was lost. This means synthesizing data from intense research with stories from his childhood, and the juxtaposition of academic truth and emotional truth come together to form a powerful account.
The Armenian Genocide
In addition to the already-overwhelming evidence he provides as to why the Armenian Genocide was a horrendous mistake by racially-prejudiced and hateful murderers, Balakian also discusses the genocide for another aspect. Ironically, the public knowledge about this crisis went ignored, and he makes a fair case connecting the Holocaust with the Armenian Genocide. In order to understand this, the genocide has to be appreciated within a broader category of racism which includes both Armenians and ethnic Jews which were both despised by myriad racists across Europe.