The woman’s shyness
The narrator's closest cousin is naturally shy. Ironically, the woman is bold while interacting with strangers but shy with people who know her. Paradoxically, the narrator's cousin gets comfortable with strangers, and she does everything possible to avoid relatives. The only relative the woman is comfortable with is her cousin, who is the narrator.
The irony of Buddy’s old friend
The primary irony is that the narrator’s friend is an old woman with white hair, but she behaves like a child. Despite being an old woman, she plays kite flying and paper decorating a tree with the narrator. The reader realizes that the old woman acts enthusiastically like a child, and she blends very well with the narrator because they do similar things and think the same way.
The paradox of the purse
Initially, when the narrator sees the purse under his cousin's bed, he thinks it is empty because of its old condition. Ironically, when his cousin comes in, she pulls out the purse, and it is full of money she has collected from selling cakes and charging people who often come to see the deformed chicken. Consequently, the narrator concludes that looks can be deceiving.