While in overall numbers the allied forces nearly matched the Chinese, T. R. Fehrenbach explains (in This Kind of War), at the point of impact the disparity was overwhelming:
But the terrain made it a series of Indian fights. While one American division was cut to pieces, others a few miles across the mountains enjoyed relative peace and quiet.
Understandably, American commanders were eager to get out of the horrible mountains and back to where they could fight once more in modern, civilized fashion.
The first withdrawal, to the 38th parallel, would have accomplished this. But the retreat once started was difficult to halt.
[...]
Contact, except for scattered patrol actions, was broken. The mechanized U.N. forces had been able to move south faster than the footsore, ill-supplied, and badly coordinated CCF could follow.
Now geography began to exert its influence in reverse. In South Korea the terrain was still broken, but passable to vehicles. In a narrower part of the peninsula, Americans and ROK’s could throw a continuous line from coast to coast, with a refused flank to either side. And while U.N. supply lines were shortened and improved, the CCF inherited a logistic nightmare.
The CCF’s guns, ammunition, and supplies had to be brought down from the Yalu under constant air attack, over poor roads, and on a limited amount of transport. The CCF had manpower, including thousands of Korean laborers, and could live on very little, but there is a limit to the operations of an army that has to bear its ammunition hundreds of miles over mountains, principally by muscle power.
Now, rebuilt, reequipped, in maneuverable terrain, the U.N. forces needed more than anything else the will to fight. The means they had.
Matt Ridgway supplied the will.