Contrary to your version of "history", the Korean peninsula was divided between US oversight in the south and Soviet oversight in the north after WW2. When US troops withdrew in 1950, North Korean troops invaded the south and nearly conquered the whole peninsula. That's when the UN sent in troops from dozens of countries, including many from Canada, though the US was by far the largest contingent. UN forces pushed the N Koreans back across the Yalu River, which is when the Chinese jumped in and pushed the front south again to its current position.