Identity as a spectrum
Dramatic irony keeps Ernesto from understanding himself except as he experiences himself in daily life. That just means that different situations show him aspects of his own character that he did not know about; there is such a thing as drama of one's own experience of self. In this case, that drama is primarily depicted as individualism. Take away the motion of the narrative and consider only the beginning and end; in the beginning, he defines goodness as a self-sacrifice for his community. And at the end of the plot? When the novel is over he is almost completely individual.
The Mexican government irony
The US government is not an innocent government, but just ask a Mexican family about the government some time. The Mexican government is historically defined by corruption and for its policies which harass the people for the profit of government officials. This unstable government cannot keep its power while disenfranchising the whole nation, so eventually there are rebellions. This means that the government needs to draft an army. When Ernesto's town is visited by newcomers, the people head for the hills; they know it is the government come to force them into the military.
The sudden isolation
This story is like an exile story, similar to the diasporas of the Bible. This diaspora sends Mexican communities out into the north like the particles of a gas that just started to boil. They stand a better chance of adaption and survival if they betray their emotional preference for community and flee only a few people together at a time. Suddenly this community which was defined by its intimacy and the shared sacrifice of the people is fractured; all the community will suddenly have to face difficult life transitions and this time, they will not have their community support.
The death of mother
Ernesto's mother dies, revealing to him the dramatic irony of death. This does two things; it radically changes his life so that he cannot ignore his mother's death for very long, and it immediately reveals to him what stability and grace he was afforded because of his mother's sacrifice and contribution. Without her protection, his life becomes very uncomfortable and he is suddenly asked to accept more responsibility than he can bear. He ends up in a serious fatigue and existential dread.
The school irony
Although typically education is treated as the holy grail of Mexican novels, this novel frames school's benefits within the frustrating dynamic of an irony. The irony is simply that Ernesto is not automatically afforded equality and opportunity just because he succeeds in school. Ironically, nothing really comes of his education. By far this version of the story is more normal; the stories where fate finds someone in high school and whisks them away on the adventure of their life—such fates do occur, but Ernesto's path is the everyman's path. He is not saved from his boring life as a second-class citizen in a land that is not his home. School is a powerful tool in his coming of age, but it does not "solve adulthood" for him.