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Why I regret using 23andMe: I gave up my DNA just to find out I’m British | Technology | The Guardian
(www.theguardian.com)
This is a most excellent place for technology news and articles.
I mean you've basically hit the nail on the head except you're misunderstanding one important thing. They aren't 'trying to find one' they have one. Their culture IS that Irish or Cuban heritage and it wasn't retconned from 23andme or ancestry.com - it comes from the story they were told about their identity by their parents from an early age.
But they're not Irish or Cuban or Italian.
They're Americans.
Emphasis on "heritage".
I guess both 'identity' and 'heritage' are doing a lot of heavy lifting.
And I know this is mostly pedantry, but there're terms that actually do fit better. Like immigrants, settlers, etc.
My great grandad was from Sicily. I'm from Minnesota. I don't have any heritage or identity that has much to do with Sicily. I do have heritage as the progeny of immigrants from Sicily. But not Sicily.