Like being American for instance.
I think that patriotism, being proud OF the United States, and being appreciative of all that Americans have done in our history, is different from being "proud of yourself" because of being American. An immigrant who has experienced hardship, worked diligently, and persevered through the process to become a citizen could certainly be proud of "being American" because his nationality is an accomplishment.
I think we often use the words "proud of being" something we were born (black, American, Mexican, Indian, tall, pretty) when what we mean is that we are not ashamed of characteristics, including nationality/ethnicity, that are independent of our personal character, behavior, and achievements.
When we say, as in the song, "I'm proud to be an American," I think it means, "I associate myself with all the good things America stands for, and I commit myself to participating in what the best Americans will do."