No, I see no reason why people who are more comfortable with another language shouldn't be allowed to use it. That being said, I think that immigrants should be required to learn English because it's practically necessary in order to be successful in America.
Legally they're not required, but de facto, to really get anywhere in America, you have to learn English. By the third generation, immigrants almost always know English better than their native language, even if they live in an area that's kept the native language alive as well. There's not really a point in legally requiring it for the sake of nationalism when it happens by definition and has plenty of support already.