Benjamin may have Asian-American cultural heritage, but he is not an Asian-American person. As Ronnie says, genes are what determine your race. You can't wake up one day and decide that you feel a different race than what you are. His race is white. It's possible that his culture is Asian-American, but that's a very different thing. He says that he shouldn't have to keep pretending that he's a white man, but he is a white man. He's a white American man raised by Asian-American parents.
Benjamin has a different take on things. Where he grew up, everyone referred to him as Benjamin Wong and knew that his parents were Asian-American. They treated him as if he himself were also Asian-American. That is the culture that he grew up in and was influenced by. Certainly, he has some claim to it.
Words have meaning, and those meanings are often politically charged when race is involved. Benjamin himself would never be discriminated against in person for being Asian-American. He can live with the cultural influences as much as he wants, and still he won't be forced into the roles that a race-conscious society puts on Asian-American people.
Calling the electric violin a fiddle gives it an identity that it isn't. They may look the same, but they aren't producing the same type of music. The cultural meaning is different. Ronnie objects because calling his instrument a fiddle gives it—and him—a type of cultural significance that he rejects.