Every minority group has its code words. Think of the phrase American born Chinese (or ABC) as Chinese American code for kids born in America but of Chinese descent. "But wait!" you're thinking. "Shouldn't that be Chinese born American because you're Chinese, but born in America?"
Yeah, well, no. And here's why. Putting American first emphasizes that the person is American, and that's really important to Chinese Americans because historically they've often been viewed as foreign—or Other—and therefore not American.
Need an example of this in the book? Just take a look at Jin's anxiety about Wei-Chen when they first meet, and Danny's anxiety about Chin-Kee. The way Wei-chen and Chin-Kee look and sound clearly make them seem foreign (especially Chin-Kee, whose clothes look like they're from 1800s China).
Or you can hear it straight from the horse's (okay, more like author's) mouth.
Then there's the born Chinese part. Think of this part of the phrase as a sign of native pride—it's like saying (if you're Chinese American) that you'll always be genetically and racially Chinese, that your Chinese roots will always be there no matter what you do to yourself. You know, kind of like a brunette who dyes her hair blonde—sure she might be blonde on the outside, but once that dye job starts to fade, those roots have nowhere to hide.
Another reason why CBA doesn't work? It's not ABC. Really—what good is an acronym if it isn't catchy? Plus, ABC reminds folks that Chinese American people know their ABCs, sometimes even better than they know Chinese.