I've been lurking here for a week or so (great site!), finally registered and wanted to reply to this topic straightaway.
As a person with a somewhat complex background (born in Germany to U.S. parents with different ethnic backgrounds; raised in Germany and have lived in multiple U.S. states) I only share what's relevant. Usually people who are interested inquire further and I'm happy to oblige them. I can only imagine what's it's going to like living in London and trying to explain how I ended up there...sigh.
US-American history and the rationale for differentiating ourselves by ethnicity are somewhat unique. While our American neighbors, even with similar histories of massive immigration, subjugation of natives, and slavery eventually solidified their national identities around a set of ideals that every citizen was encouraged to embrace (and were accepted once they did), the U.S. actively excluded various immigrant groups, often based on a racial hierarchy that put English culture (aka White Anglo Saxon Protestant or WASP) at the top and whatever other nationality or ethnic culture in opposition (i.e., Germans, French, Irish, Italian, Jewish, Chinese...). Some ethnic groups have never been fully accepted (basically groups with recent African roots) due to the racial rules in the U.S. There are also places in the U.S. where ethnic cultures are extremely vibrant and meaningful and people did not need to 'assimilate' in order to succeed. Lastly, with the renewed focus on ethnicity and ancestry, more people who come from the most assimilated/mixed backgrounds have started to become more interested in being more than "just American," so it becomes meaningful to be 1/16 of X and 1/32 of Y.
So basically ancestry is relevant to US Americans for one or more of these reasons:
1. They were raised in an ethnic enclave where their immigrant culture remains strong and distinguishable from the mainstream WASP culture in their region (i.e, Cubans in South Florida, Germans in Wisconsin, Polish in Chicago, Italians in NYC, Creoles in Louisiana, Mexicans in the Southwest)
2. They belong to an ethnic group that was once despised and heavily discriminated against by the WASP establishment (i.e, Italians, Jews, Irish Catholics, Chinese), so their immigrant culture(s) made them different from "regular" Americans
3. They have African roots and ancestors were slaves, African immigrants, or from the Carribean or South America
4. They were in raised in families that fully assimilated and that seems boring, so they are reclaiming an "interesting" background
What most US Americans only realize by leaving the country is that (generally) the rest of the world sees us as "Americans," which is different from how we generally see ourselves. I can't tell you how many Black Americans I know that come back from Africa or South America and are shocked to find that people treated them like the foreigners they are. We are just so used to having to distinguish ourselves ethnically that we don't understand how insignificant or nonsensical these distinctions are to non-U.S. people.
Just like it might matter in Britain what social class one belongs to and no one in the States would care because you're "just British," the same principle applies here. I suppose it would be really annoying to me if the British living in the U.S. insisted on discussing social class, but I'd probably just chalk it up to cultural differences.
