Chronology and narrative
The novel uses a plot devices that make the narrative anachronistic; the reader sees the end of the story first without seeing how that ending resolves, and then through a lengthy series of flashbacks, the novel concludes by showing the reader what Beka makes of the death of her friend. In other words, the novel is clearly showing a problem and then its solution instead of using a chronological approach to narrative. Another irony is that the irony starts and ends at the same time instead of transferring the reader from beginning to end.
The random politicians
There is a situational irony when the novel's detours into the side plot where two British politicians are tried for treason. What is the connection? The absolute disconnect between two school girls in Catholic school and the politicians is obvious, but there is actually a connect. The narrative irony points to symbolic connections between teenage immaturity and treason; Beka is like a lying politician in the "court" of her parents, and she feels deeply ashamed of this, but unlike those men, there is still time for her to choose a new path.
Parent and child
It is inherently ironic for a child to be so at odds with her parents although they gave so much for her. Why does she waste their sacrifice? She does it as a criticism against them, playing judge in the home. This irony seems shameful, but it is a natural part of life; her journey toward adult sincerity begins with her enmity with her parents. That conflict is like her conflict with fate, or perhaps even her conflict with God. She feels pressure from school authorities and family authorities to perform, and she resents that before eventually realizing that they are doing what is best for her in their opinion.
Catholic school and irony
The girls' experience of Catholicism is ironic and counterintuitive; instead of being a pillar for their faith, the school begins to push them away from religion by constantly shaming them into slavish obedience to strict rules that are unnecessarily dour and archaic. The girls are naturally prone to explore, to learn, and to be curious (which is naturally similar to education) but the school pushes them away from knowledge as well by framing that knowledge in a classroom setting that is insulting to the girls' pride as a result of classroom tyranny.
The drama of dishonesty
The dramatic irony regarding Beka's honesty is a painful conundrum for her parents who are not stupid enough to believe her. This happens because she insists on her lie. She knows how to double-down—that's for sure. The difficulty is painful because she can twist the criticism around by exploiting their suspicions about her. She is able to pretend that their suspicion is not an honest reflection of her character, but of course when she is inevitably discovered for her dishonesty, the truth is plain.