East Asians, including Koreans came from the lineage of Caucasians; they inherited straight hair and fair skin from them. They're not trying to be 'white'... a lot of them are 'white' as they inherited fair skin from Caucasians.
Also, i'm a Korean myself ansd the answer is really simple: Koreans just simply prefer and strongly think that 'white skin' is really nice-looking and much prettier than dark skin, while white people in Europe and the United States prefer tanned skin.
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