South Korea on its own couldn't conquer the North, but if there were no Chinese intervention, then the US-led forces could take the North. The hard part is changing Mao's mind, so that he thinks intervention is too risky.
In the CCP Politburo there was considerable opposition to intervention, some members "arguing that the enormous tasks of reconstruction and reform in China required vast resources and the energetic attention of the people at al levels. They also stressed the lack of adequate equipment for the Chinese troops. But Mao remained unshaken in his assessment that there was no other way. 'Your arguments are based on good reasons.' he said. 'But all the same, once another socialist nation is in a crisis, we would feel bad if we stood idly by.'"
https://books.google.com/books?id=vg4CuFmpkCEC&pg=PA145 With Mao standing firm, the Politburo eventually gave way, even though Lin Biao was among the doubters.
"Mao Zedong seems to have been in little doubt that the PRC would have to intervene for the sake of the Korean revolution and revolutionary movements elsewhere in East Asia. But the majority in the Politburo and among the PLA leadership had serious reservations about sending Chinese troops to Korea. Civilian leaders such as Liu Shaoqi and Ren Bishi feared that a new war would throw up immense difficulties for a gradual and well-organized reform process in China. Many military leaders, including Lin Biao, thought that a Chinese offensive in Korea would be logistically and tactically difficult, and could endanger Chinese security in Manchuria and in areas along the coast. For both groups the prospect of an all-out war with the United States must have loomed large: Just as the Chinese revolution was being completed in spite of the constant danger of imperialist intervention, Kim and Stalin were asking the CCP to go to war by their own will with the most powerful imperialist nation in the world.
"At the extended Politburo meeting on 2 October no clear-cut decision could be arrived at, and it took at least three more days of intense discussion before Mao's line won out. The three core arguments that the Chairman put forward in favor of intervention were the CCP's debt to the Koreans who had fought with them during the Chinese civil war, the U.S. threat to Chinese security, and the availability of Soviet support for the war effort. But beyond the persuasiveness of each of these points, it was Mao's immense prestige in military and political affairs that won the day. Mao was the leader who had brought the party victory in the civil war. Even when they disagreed with him, as the majority did in the crucial case of intervention in Korea, his colleagues in the CCP leadership were willing to defer to his wishes, since Mao alone was seen to have the strategic vision that could make the party achieve its political aims...." Westad, *Decisive Encounters,* p. 325.
https://books.google.com/books?id=JBCOecRg5nEC&pg=PA325