>>32
It comes from "Goguryeo", the name of an ancient Korean empire, which is thought to derive from words meaning either from "walled city" or "center." Curiously, the latter would give it pretty much the same meaning as the Chinese endonym.

>>29
An experiment for you: The word 'negro' simply means black, from the Latin nigrus, and terms with shared etymology remain the accepted label for peoples with dark-colored skin in several European languages. Go to the projects and explain to them why there's no logic in getting uppity when someone calls them negroes. Chicks will dig the scars it earns you.

Terms that become 'offensive' don't always follow logic. In the case of Shina it appears to have possibly been because the kanji used were thought to imply subservience. Ironically, this is the very reason the Japanese (at that time the 'Wa') changed the Chinese character used to write their country's name from 倭 to 和 in the 8th century.

In any case, I'm not sure why a name of a single dynasty perpetuated as an exonym by the works of Marco Polo makes a 'more consistant name' than a sobriquet that's appeared in Chinese writing for well over two thousand years.