Why is ‘Caucasian’ derived from the Caucasus?

Why did the word 'Caucasian' come from the Caucasus, if people from there tend not to be Caucasian?

The Greater Caucasus Range, running northwest to southeast between the Black and Caspian Seas, is the traditional line of demarcation between the continents of Europe and Asia. Linguistically, culturally, and even ecologically diverse, the Caucasus area is home to more than 50 ethnic groups and is one of 34 "biodiversity hotspots" (areas with significant, threatened biodiversity) in the world.

Source: Ancestry

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In the 19th century, the term Caucasian referred to both light-skinned people and dark-skinned people as you would find in India. It was only in the 20th century that this term acquired its "specialized" meaning of "of European descent," especially in the U.S.

In the racial classification developed by 19th-century anthropologists, Caucasian (or Caucasoid) included peoples whose skin colour ranged from light (in northern Europe) to dark (in parts of North Africa and India). Although the classification is outdated and the categories are now not generally accepted as scientific (see Mongoloid), the term Caucasian has acquired a more restricted meaning. It is now used, especially in the US, as a synonym for ‘white or of European origin’, as in the police are looking for a Caucasian male in his forties.

Also see what Webster's Dictionary's entry on Caucasian has to say about this word:

Caucasian vs. white

Caucasian has two fairly distinct meanings, and the difference between them occasionally leads people to aver that one of them is incorrect. The earliest sense of the word is a literal one: “of or relating to the Caucasus (a region in southeastern Europe between the Black and Caspian seas) or its inhabitants.” The second refers to the racial group commonly referred to as white.

The objection to using Caucasian to refer to a white person is that many whites do not actually come from the Caucasus region. Be this as it may, there is no rule in language stipulating that the formation of a word must be based on logic; were this the case we would not call members of this racial group either Caucasian or white, since there are very few whose skin color is in fact that exact shade.