Stalemate developed along the Western Front because they tactics of offensive warfare had not developed while the technology of defensive warfare had.
The invention of the machine gun, especially, had made it so that headlong charges of masses of soldiers were suicidal. But the heads of the armies had not figured out any ways to attack that did not involve frontal assaults.
Because of this, they got bogged down in the trenches with no way to maneuver around the enemy and no way to break through the enemy.
You could also argue that the stalemate happened because the Germans did not put enough faith in the Schlieffen Plan. But I think it is more an issue of not having enough offensive tactics and mobility to avoid the stalemate.
The "Race to the Sea" which occurred during 1915 along the Western Front led to both sides being fully entrenched and stalemated until 1917. Part of the reason the stalemate occurred in the West and not the East was (as it was again in World War II) because France was not the objective -- Russia was. The von Schlieffen plan failed precisely because Germany wished to insure its success - by committing most of its troops to the East, it could hope to defeat Russia. By fully committing troops early in the war in the West as the plan called for, overrunning France, and redeploying them to the East, Germany could have prevailed against both countries. But the German High Command feared that committing troops Westward would slow down the main thrust to Russia. By scaling back, the offensive into France failed, and the Front became defensive on both sides until later in the war. Rather than countering the French trench by trench throughout 1915, the Germans could have fully invaded and won. Poor generalship in general, and poor appreciation of current weaponry specifically was characteristic on both sides during the whole war.
The stalemate happened because Germany did not achieve the victory against France in August 1914. Fighting developed to a large extent dueling man against machine. Britain had a large industrial capacity and France and Germany had simple man power and they were not equipped with the same type of military might. In the ned the key factor that led to the stalemate was the use of tanks en masse.
Stalemates developed because of the strategy of trench warfare. It was the system of digging trenches in which soldiers would burrow into the ground for stealth and protection and lob grenades, shoot machine guns from, and throw everything from Molotov cocktails to oil soaked paper. This resulted in trench lines being built and used for weeks in which troops did not move in which it seemed like a stalemate, even if progress had been made. It is similar to the current system of fox hole strategy used in WW II, but this strategy used a single hole per soldier instead of an entire line of holes for divisions.