I think it's very important for Chinese people here to be united, afterall we share some common background and common interest. Chinese american can only be stronger and have more political or economical clout as a group. And our next generation carries certain responsibilty for this as well. Look at Jews. As someone here said already, you may be an American citizen, but you can not change the fact that your ethnic background is Chinese.
Also right now the world is moving towards globalization, American culture and chinese culture are quite different in many ways. Knowing both of them will be beneficial to you as well as to the society as a whole. Of couse you can argue that for this logic, you can pick up any other second language, like Spanish, true, but with Chinese, you already have a great advantage.
I think both Chinese and american culture have many good things to learn from.
Interestingly, I know quite a few American couples who adopted Chinese girls. They are taking troubles to take their kids to Chinese church and/or Chinese schools.
When my kids grow up, I want them to feel proud being an american citizen as well as a Chinese. With more exposure to diverse cultures, they will be less likely to be biased or narrow minded.