> Jews are not “white”
In classical racial theory terms, Jewish people, as a (sub)racial group are, actually, White (the subcategory hierarchy running, from the top, Caucasian -> Mediterranean -> Semitic -> Jewish.)
Now, its true that despite classic racial theory being intimately connected to various forms of White supremacy, most actual forms of White supremacy include bigotry that operates on different levels than classic races, and treats lots fo White subgroups as either non-White or inferior within the broader White race, but that’s a side issue. “People of color” has never been intended to mean “every group marginalized by the particular people adhering to White supremacy in the immediate social context”; it is fairly inclusive, but its not intended as a catchall, and exclusion of people from that label is not discrimination against them.
> My go to theory, is that some people, who are not quite clear of racial biases, wanted to have a name for specifically and strictly for black people, but without ever using word “black”.
Actually, he term was one of many used during the period of de jure discrimination to refer to people of black ancestry (in some times and places, like “mulatto”, with precise legal definitions which distinguished it from “black”.)
From there it was one of many terms adopted to varying degrees within the community of black ancestry (sometimes, as equivalent to “black”, and sometimes, within some corners of the community that use “black” more narrowly, with a broader definition.)
It faded as an identity label within that community, and was recycle for broader use fairly recently (“black and brown” has been used in a fairly similar sense for a longer time, and still has considerable currency; a lot of activists will use “black and brown people” as the general collective term, but something like “woman of color” when referring to an individual – actual or hypothetical – person.)