Catherine is Manjiro's girl. Well, okay, not exactly—it's not like they're official or even going out. It's just clear that Manjiro likes her and she likes him back. She even tells her friends that she's willing to marry him.
Sounds sweet right? The only thing, though, is that we don't really hear from Catherine after Manjiro overhears her conversation with her girlfriends. Why? Well, it's not Catherine's fault—she's still the sweet girl Manjiro falls for—but her friends, on the other hand, are not so sweet. They point out: "Your parents would never allow it. Think what people might say!" (3.24.58) You know, because it's inconceivable that she could ever be with a Japanese boy to them. Ugh.
As a result, Manjiro runs off, torn apart by disillusionment: "His heart rose into his throat. How could he have been so foolish? How could he have thought he was one of these people? That he could be an American?" (3.24.59). While this may seem like it's about a crush, though, it's really about something more.
Catherine represents two contradictory situations: first, that Manjiro can be an American and fit in because Catherine likes him enough to marry him; and second, that Manjiro can't be an American because other people around them would never accept a romantic relationship between he and Catherine. It's an important reminder that though Manjiro thrives in America, the country is still not truly a home for him.