Why Do Germans Say “With a Migration Background” Instead of “[Ethnicity]-German”?

American here. Can someone explain why in Germany people often refer to migrants as “[person/people] with a migration background”? It seems pretty vague (and also kind of a mouthful). When I’ve visited Germany, I’ve noticed they don’t typically use terms like “[ethnicity]-German” (e.g., “Asian-American” or “African-American” like we do in the U.S.).

For instance, I recently met a German of Pakistani descent, and he described himself as “having a migration background” rather than saying “Pakistani-German” or simply “German.” I get that this is a personal choice, and I know the hyphenated identity in the U.S. can also be criticized for reinforcing white normativity, but I’m curious—why is this phrasing so common in Germany?

Edit: The responses here have been enlightening. To clarify my question: As someone connected to Germany through marriage and frequent visits, I deeply respect Germany's intentional move away from racial categorization given its history. However, I'm curious whether the formal, bureaucratic nature of 'migration background' might sometimes obscure rather than address real experiences of difference in daily life. I'm not suggesting the American approach is better (it has its own significant problems), but rather trying to understand how different societies grapple with discussing diversity and belonging.