I have already explained.
South Korea is NOT a suitable logistic base (THE ENTIRE COUNTRY) because they don't have suitable road or even railroad back in 1950s. South Korean back then is like a giant farmland with a few big city in between (Seoul, Inchon, Nakdong and then Pusan) that also explained why North Korea can just ride thru the entire country from the north and reach Busan in around 3 weeks. You don't have a lot of build up area and road network for you to put defensive position, If South Korea back then is like Ukraine now, the South can do what the Ukrainian do and wage a 3rd dimension attack mixed with conventional war and insurgency. The South Korean can't, that is why they folded that quick.
As I said, if the UN wanted to set up South Korea in a way you can sustain fighting on, THAT alone is multi-year process. That is why it took them 3 years to build up the supply and are able to fend off the Chinese+NK attack which is something they CAN'T just 3 years before. If the South Attack North now, they can and will have enough supply base and road network to support a war further north, unlike back in 1950. Had the war last into 1960, that would be another issue, we may actaully see South Push North and regain some ground, which evidentially is what happened in the last 3 months of war. The South don't want to end there because in the last 3 month, they took a few village in the North at the last couple of month and that contributed to North Korea losing 1500 sq mile of land to South Korea.
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That entire war is a war of supply, it's between how US turn South Korea into a build up defence and make road. And that applies the same to the Chinese Troop, they had exhausted their supply line, that is why they were stopped at Han river, on the other hand, just because UN troop may have advantage on logistic (they really don't because again, you are talking about a few hundred mile supply line for China to over 5000 mile supply line for UN troop) it does not mean the can overcome the supply issue and overwhelm the Chinese troop. Chinese Troop cannot advance does not mean they need to fall back, if China can supply their troop on the frontline, which is independent to what UN logistic capability.
So no, Chinese Troop is NOT the direct reason why UN retreated in Dec 1950. Chinese troop influx triggers a LOC problem so dire the UN cannot overcome, which leads to the UN troop withdrawal. They gamble the operation is quick and they gamble the Chinese will not move, they lost that gamble. That does not mean Chinese troop "Defeated" the UN. You can put in extra 300,000 of anyone, Chinese, Russian. Vietnamese or Mongolian, the reason is going to be the same.