There is a limit on how far should you take the significance of your origin: whatever-American.
The US is an immigrant country so when a person make known his/her origin, what is he/she saying about it ?
On the one hand, since the US is an immigrant country, a person's origin implies that the US minimizes that origin. How you make it in the US depends mostly on yourself. That does not mean there are no social barriers in the US that may adversely affect a particular origin, every ethnic group have its own bits of 'horror' stories of those social barriers. But what make the US different from other countries/societies is that those social barriers do not have as much legal support when compares to other countries/societies.
For example, how many countries in the world have automatic birthright citizenship ? Not very many. Citizenship endows a person with legal privileges and responsibilities that make that person the legal equal of fellow citizens. The current interpretation of the 14th Amendment in the US Constitution effectively erases a person's origin as far as the Constitution is concerned. Everything about the person's origin, especially significant items like race/ethnic and religion, are meaningless to the Constitution.
On the other hand, there is a danger in bringing up one's origin in that America could not have got the way she is today unless there are unique contributions from one race/ethnic group that does not exist in other race/ethnic groups. That dangerous implication/insinuation is real and is a constant threat of division in America. Division in the social, legal, and political spheres.
For example, so what if I am an Asian-American ? Is there something 'Asian-ness' about me that does not exist in 'Italian-ness' ? Are Asians more hard working than Italians ? More physically beautiful ? More intelligent ? More of everything ? As an Asian-American, my favorite food is pizza and it is American style pizza at that. I have been to Italy and know Italian style pizza. I just like American style pizza better.
My point is that there should be a limit on how much significance one should place on one's origin. As Americans, we should all focus on what we are as Americans in general and that when a person brings up his/her origin, it should be to emphasize how America frees the person from the many types of shackles that origin may have had upon that person should he/she remains in his/her country/society of origin.
I find it easy to say 'Be proud of where you came from'. Every country and society have things they are not proud of, in history and current status. When you claim association, this is not a buffet table of things you can chose to be proud/ashamed of. The whole table is yours and you have to eat everything. Am not saying you should not be proud of your origin, but I am saying that origin's significance should be in the your current context.
Like it or not, the fact that you are here -- in America -- begs the question: 'If where you came from is so great, then why are you in the US and is a citizen ?'
And like it or not, the fact that you are here -- in America -- and is a citizen means that where you came from is not so great after all.
What make the US a great country in every sense, from geography to social to political, is the fact that we are free to discard our origins if we wanted to. Does not matter if you are proud or ashamed of where you came from. Proud or ashamed is your deeply personal freedom of choice and is as private or as public if you want. Just like your past association, if you want to associate yourself with America, you have to eat the whole table, from institutionalized slavery to emancipation, from a bare continent to a country that went to the Moon, everything good and bad about America is yours.
You do not like this table ? Go back to where you -- or your parents -- came from.