From my understanding, whiteness was even a European thing, excluding Italians and Irish, who are both 'white' skinned. And today I'd consider that Asians are considered 'white' by some (from my American pov). But how did that happen?
There's a fantastic recent book on the global construction of "whiteness" by Marilyn Lake and Henry Reynolds entitled Drawing the Global Colour Line: White Men's Countries and the International Challenge of Racial Equality. To provide a short summary, the concept of "whiteness" was often linked to power and social status historically, which is one reason why Irish and Italian immigrants were not considered "white" in the 19th century. Lake and Reynolds, however, argue that this was a global phenomenon, not just an American one, and contemporaries understood the issue in those terms.
One of the more interesting anecdotes from the book involves the requests of Japanese delegates at the Paris Peace Conference in 1919. The Japanese diplomats sent to Europe were furious - absolutely furious - that they were not considered "white" by the other allied powers. As an industrialized nation and a member of the winning side in the war, they believed that they were entitled to being identified with "whiteness," and the Japanese delegates made racial issues a big part of their platform. Part of the reason for this disparagement is that the experience most "white" delegates had with the Japanese (mainly through the Americans) were poor migrant populations, and they were thus disparaged as "a yellow race":
The ultimate issue was whether Japan, which had made good its title to be treated on a footing of complete equality as one of the great powers, was not entitled to rank among the civilised nations, whose citizens the Americans should accept on a basis of equality…The question which Japan raised with absolute propriety was whether Asiatic descent should permanently disqualify nations from the enjoyment of the rights fully accorded to one another by the great nations of the world (276).
I don't have time to write up a response now, but I wanted to recommend Nell Painter's The History of White People. While it does look at it from the American point of view, it discusses the mythology of race that is still prevalent today (the emphasis on the Caucasian, the furor over white slavery, and this Teutonic ancestry, among other things).
hi! there have been a few threads about this; see these for previous discussions
How did the concept of "whiteness" as a racial identity develop and change over time?
When and how did ethnic groups such as Irish and Italians become "White"?
... and I'm sure there are several more