One way to approach this is to consider what the themes of the novel are and how the relationships between characters help explain that theme.
Gogol resents his family when he's young because he doesn't feel like he truly belongs to Bengalese culture. He doesn't like his name—after a Russian author his father admired—and disconnects from his parents and heritage. He prefers to be more American than Bengalese until his father dies, at which point he becomes closer to his mother and sister, accepts his heritage, and marries a Bengalese woman.
One theme of the novel this helps illustrate is cultural identity. In order for Gogol to reject Bengalese culture and participate fully in American culture, he has to reject his family. His parents want to have a relationship with him, but he sees his family as part of the cultural practices that he longs to escape. You could talk about the tight bonds between older family members and cultural traditions, as well as how restrictive these practices...
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