Despite a strong US and UK commitment, and an only tepid Soviet presence (I think, could be wrong, but IIRC Stalin had been against the war, and only supplied equipment and fighter pilots, while Mao was the one that basically fought the war on Kim’s behalf), they were pushed back and we ended up with that notorious stalemate. How exactly? What were the precise logistics of this failure, what was the turning point, and if there are dissenting views on this, what are they?
Sorry for my overly inquisitive tone. I’m just curious.
A couple of key reasons exist as to why the UN forces, mainly the US, was unable to solidify and hold their gains on the Korean peninsula north of the 38th parallel after the successful amphibious landing Inchon and their drive northwards.
First, while the UN forces were able to effectively cause the North Koreans to rout after the successful landing and subsequent battle at Inchon, MacArthur and his subordinate leading X Corps, Ned Almond, failed to effectively trap or destroy the fleeing North Korean forces. This caused a variety of issues, mainly allowing the enemy to fight another day, as well as embolden Mao/China to eventually support North Korean forces militarily in their drive to the 38th Parallel.
Second, after UN and US forces led by MacArthur and Almond took Pyongyang, they continued their pursuit of the retreating North Korean forces moving north to the Yalu River/Chinese Border in an attempt to rectify their earlier error in not trapping or encircling North Korean forces. Despite several warnings from the Chinese government that any operations north of the 38th Parallel would be seen as a direct threat against China, the US/UN continued their drive northwards. The Chinese Politburo eventually decided that if US/UN forces proceeded to reach or come close to the Yalu river, military action and support for the North Koreans against UN forces would be inevitable. Despite warnings being issued by the Chinese government to the UN through several channels, UN forces continued to move closer towards the Chinese border/Yalu river. They also proceeded to conduct several reconnaissance flights of the Chinese side of the river as well as some disputed reports of combat air missions being carried out against hostile forces within Chinese territory.
At the same time, both MacArthur and Almond allowed their forces to keep up their pursuit of NK forces despite not taking the time to consolidate gains they had already made on the Korean peninsula as well as strengthen supply lines or lines of defense as they made their push northwards. Their mistake in not doing so became all too clear on October 25th, 1950, when Chinese forces entered North Korea and began to push back against pursuing UN forces after the aforementioned reconnaissance flights as well as the growing UN presence just south of the Yalu river. The sudden inclusion of 200,000 chinese troops into the Peninsula quickly turned the tide against the technically and materially superior but numerically inferior US led UN forces.
The final factor I'd point to as to why the UN forces were so quickly forced to retreat to the 38th parallel after having taken so much of the peninsula was due to the early onset of the Korean winter, which was unanticipated by UN forces. Many combat units were still not equipped with winter gear despite the knowledge that Korean winters could be incredibly harsh and unpredictable.
These factors are what I and many historians point to as the reasoning behind why the UN was forced to fight and eventually accept the stalemate at the 38th Parallel nearly three years later.
Sources:
The Coldest Winter: America and the Korean War by David Halberstam
At the most basic level, a third of a million Chinese is a pretty hard counter-attack to stop, when your entire amount of forces all over the country isn't quite a half-million. Combine that with the fact that people didn't want to believe that the Chinese would actually interfere, so no significant attempts at preparation were made, and that turned into quite a nasty surprise.
The US Army's history site goes into it a reasonable bit. http://www.history.army.mil/brochures/kw-chinter/chinter.htm
See also. http://www.history.army.mil/html/books/021/21-1/index.html and http://www.history.army.mil/html/books/021/21-2/index.html
First, let me address a few points in your question. There were NO Soviet forces in Korea, save for MiG pilots, and even then, they were involved in secret and were based only in the far north of Korea and in China. Stalin's support of the war was tepid, at best, but it wasn't until he gave the green light that Mao got behind Kim and that the war was able to start. If Stalin had said "no", the war wouldn't have happened. Also, I wouldn't classify the Korean war as a "failure" - the military goals were achieved. The South was saved from northern aggression. Period.
Politically, the UN mandate was to stop North Korean aggression and to save South Korea. It was NOT to re-unify the peninsula. MacArthur was able to push his forces north because a) the North Koreans had been routed, b) the Chinese had NOT entered the war at that point, and C) who was going to tell MacArthur no, or more specifically, who would MacArthur listen to? By January 1951, MacArthur had overextended his supply lines, his forces had been destroyed, physically and psychologically, and they had been pushed back south. With General Walker killed in a car accident, General Ridgeway came to power and was given a free hand by MacArthur to do what he needed to do. Once MacArthur was finally sacked, Ridgeway became the overall commander and he was a guy who followed the chain of command. The orders were to push the communists out, but re-unifying the country was NOT the goal. By mid 1951, peace talks began and they dragged on for two more years while both army's simply held their ground.
Militarily, the Chinese and the UN forces were opposites. The Chinese had manpower but no technology. The UN forces had the technology, but a finite amount of people. The Chinese were able to throw waves of people at the UN lines, and the UN lines were able to use heavy machine guns and napalm to mow them down. Neither side was particularly eager to push harder than they needed to to maintain their positions. From mid 1951 until 1953, the front didn't change much with a few exceptions - Baekmagoji and the Punchbowl being the big battles after 1951 where some significant real estate was traded.
Further, militarily, the Chinese had the advantage. The UN forces were used to fighting in Europe - fairly flat, good roads, a mechanized armies playground. In Korea, the roads were terrible and the country is a giant mountain range, especially in the north. The UN forces committed themselves to staying on the road - their tanks, trucks, and artillery could not leave these arteries. The Chinese on the other hand had marched all over China and they did the same in Korea. They were not bound by the roads and they were able to bypass major UN forces by simply walking through the forest and the mountains. The UN was able to maintain a grip on any road it wanted and the land surrounding it, as long as it was flat and clear. The Chinese were able to hold any mountain and gun down UN forces below them with virtual impunity.
TLDR - the UN forces were overwhelmed by the Chinese entrance into the war. While they had conquered most of Korea by November 1950, the UN forces had overextended their supply lines and the Chinese, using superior numbers, tactics, and knowledge of the type of fighting necessary, were able to push the UN south of the 38. The war was a a victory for the UN - they stopped North Korea's aggression and saved the South which was their goal. Korean political leaders and MacArthur might have called it a failure, but that's their view on it.
The two go-to books on the Korean War are The Coldest Winter by David Halberstam and Scorched Earth, Black Snow by Andrew Salmon. These two books cover the first year of the war from the US and UK/Commonwealth point of view.