It all started with a dude looking at skulls, he saw one that was the most symmetrical, the best looking skull he ever saw. He decided it must belong to a white European, as they are the best people (/s). He finds out that the skull was that of a person from the Caucus mountains.
Caucasian has been used to describe the ‘superior’ white Europeans since. So, OP is using the word correctly really. They say African, Asian, Latino because those are other races… with unpleasant skulls.
This is a gross oversimplification, but one of the modern excuses for racism and race superiority. Also, why ‘Caucasian’ is used to say white European.