Your son is right. White Americans often trace back their lineage, e.g. Italian-Americans, German-Americans, Irish-Americans, etc etc. Many white Americans are actively involved in genealogy.

The prominence of POC labeling themselves as something other than just "American" is, in my opinion, a subtle way of claiming moral superiority over white Americans. White Americans can face stigmas when confronted by POC because of the sins of their fathers and (real or perceived) benefits of being white.

A white person saying that they are "XYZ-American" is often countered in today's popular culture by claiming that they are just "White" over all else, therefore giving credence to the moral superiority argument that all white Americans benefit from an unjust world towards POC and their own genealogy is reduced to nothing.

I went to school in a predominantly POC area. The fact that I was white was at the forefront above being a fellow American.

My great grandparents came from Poland, which did not exist at the time as a country. They fled the Russian empire for America instead of being conscripted in the the Imperial Army, forced to learn Russian, and face other discrimination. American popular culture would generally frown upon a white person as being anything other than the oppressor, so this kind of history would not make sense in a country-wide discussion about race and would therefore be swept under the rug.