What caused North Korea to begin to push back the UN troops in the war at the Yalu River? China entered the war.
Soviet Union entered the war.
MacArthur was relieved of his duties.
Kim Il-Sung was removed from power.

Kim Il-Sung was removed from power.

Explanation:

The Korean war was a large-scale war of the 1960s, the North Korean republic had shattered and its remnants were moving back to North Korea. Causing which the ROK to force its way into the border of north and south Korea. This was followed by the UN offense into north Korea and du to which forces reached the Yalu River. Prompting the interventions of china into the war.