North Korea, China (ground forces) and the Soviet Union (air forces) were trying to take the whole peninsula, we were defending South Korea.
We won, we defended South Korea. They lost, they failed to take over South Korea. At no point did the US/UN attempt to take over North Korea as far as I know.
I agree with your assessment on Korea.
I just wish the North Korean government would collapse— its awful.
We absolutely did and do defend South Korea.
Good point.