I was watching a documentary on the battle of the hochin reservoir which was where the Chinese intervened and the Americans were forced into a retreat after killing tens of thousands of Chinese human waves.
During the documentary they kept saying how arrogant MacArthur was to be pushing so hard into North Korea and how he ignored intelligence saying the Chinese were planning an attack.
If he had heeded the warning and began to push more steadily with overwhelming numbers, could the Korean Peninsula been united under a democracy today?
The Battle of Chosin Reservoir.
No, he's not the reason. The overwhelming manpower that the Chinese brought to bear, combined with the lack of preparations by the US forces, and finally the desire of Truman and Eisenhower to end the war before it expanded into a regional war involving China officially and Japan were the reasons for the stalemate.
MacArthur was arrogant, or misguided, in his plans to invade the North. The Chinese had been sending pretty clear signals that if the UN forces crossed the 38th parallel, they would intervene, which the did. MacArthur and his people ignored those warnings and proceeded north. Now, did they do it because they were arrogant, or stupid, or because they wanted to provoke a war with China in an attempt to remove the communists from power is all a matter of debate. MacArthur was a proponent of expanding the war to China and bringing Chiang Kei-shek and Taiwan into the war, but an argument can also be made that he genuinely believed that the Chinese were flexing their muscles and wouldn't actually intervene.
Once the Chinese were involved however, it became a much different war. The Chinese had more men than the UN forces could kill, and the UN forces had more and better weapons than the Chinese could hope to overcome. That's what led to the stalemate - neither side could overcome the other sides edge - people vs. machines. Had the UN forces dedicated more men and had Ridgway (MacArthur's replacement) decided to push harder, it's possible they could have defeated the communist army. But after the disasters of 1950 and early '51, Truman just wanted to end it and Ridgway's job was to hold the line and punish the enemy to force them to negotiate at the armistice talks.
TLDR - political decisions is why the war ended in a stalemate.