A friend of mine and I had a conversation about two schoolmates of ours. Both of them are Asian American. At some point, Person number 1 ended up jokingly referring to person number 2 as a "banana." Person number 2 reacted pretty badly to this and was quite offended.
This led to a conversation about "bananas" or "twinkies" or what have you. I myself have also been guilty of calling people bananas, and thereby seriously offending them. In talking to this friend of mine, I realized that I could easily be identified as a banana. I'm an Asian American who doesn't speak my "native tongue."
It made me realize that actually, not being able to speak an Asian language makes bananas (myself included) more insecure than our bilingual compatriots. Being able to speak your mother tongue lends you authenticity, both to white people, and also to your family or your community. It seems to me that being in possession of two languages anchors your identity more concretely in both spheres, country of ancestry and country of birth, and thus you are, as another acquaintance of mine said recently, a true transnational.
As an Asian American, in possession of an Asian appearance, there are some parts of your "culture" that remain inaccessible to you if you don't speak another language. It is also pretty central to the performance of your ethnic identity. If I was home right now, I would totally dig out Rey Chow's The Protestant Ethnic and the Spirit of Capitalism, and quote it, but alas it's at home in America.
That said, I think most languageless bananas feel more insecure in their identity, I would hazard a guess, than those who are bilingual. And therefore feel the need to present or perform their identity more aggressively (that would be me) or to deny it entirely or even feel resentful or ashamed about it.