No stalemate there.
The north wanted to unify Korea under northern communist rule... they did not end up with what they wanted... therefore the only reason to sign a ceasefire agreement was because they could not change this.
The South wanted to survive and were slaughtered by the north... it was only the arrival of UN forces that stopped the norths advance and reversed to a push in the opposite direction to a similar position that the north achieved against the south.
The UN didn't want the new border to be on the 38th parallel... otherwise that is where they would have stopped and then demanded a peace agreement. They wanted a non communist Korea under south korean control. Had teh chinese not intervened they would have gotten that... but then if the UN had not intervened then the north koreans would have gotten what they wanted too.
Enter the Chinese who pushed the UN forces back to just beyond the 38th parallel... they wanted the UN supported forces of South Korea further away from their border.
You could say the North did not get what they wanted, the south managed to keep what they had, and the UN ended up with rather less than they wanted... only the Chinese got exactly what they wanted, but you say they lost...
The North started the war by invading south of the 38th as they wanted to rule a "united Korea". Their invasion and all of its goals ultimately failed.
Their invasion only failed because the UN intervened on the side of their enemy... they had basically defeated the south and then the US and her bitches stepped in.
It was a clumsy and difficult victory sure, as the opposite side was throwing too many bodies into the fight. But eventually retard-in-chief Kim didn't get his way (to rule all of Korea).
But then the UN force did not get what it wanted either... a non communist Korea... so they failed too... in fact they took most of the country only to be driven back to where everything started so their defeat is actually very comparable to their defeat of the North Korean forces... so you can say the effect of the Chinese forces on the forces of most of the western world was rather comparable to the effect of the UN forces on North Korea... and the effect of the North Koreans on the South Koreans was similar again...
But you claim the only force that achieved its objectives and moved the UN force away from its border was the outmatched Chinese.... Amusing.