There were 3 main reasons.
Firstly, by the end of 1914 both sides had constructed continuous lines of trench systems running all the way from the Belgian coast to the Swiss border.This effectively meant that neither side had any open flanks,and it was therefore impossible for either to open up the war by getting round behind the enemy.
As the months went by, the trench systems became more and more fortified, with multiple lines of trenches, deep belts of barbed wire entanglements in front, and well sited machine guns and artillery that turned the approach across no man's land into a giant killing zone.
Successful frontal attacks on such deep defences were impossible to achieve, so for nearly 4 years the front lines hardly moved.
Secondly, advances in weaponry gave troops defending such positions a huge advantage in battle.Bolt action magazine loaded rifles, belt fed machine guns, and rapid firing breech loading artillery meant that troops behind the cover of their trench systems could, quite literally, slaughter troops which had to advance on foot, in the open, across no man's land.All it was really necessary to do was for the defending troops to load and fire, the sheer volume of bullets and shells they could deliver in the space of a few minutes making even aiming unnecessary.
This increase in military firepower made the frontal attacks that the continuous trench lines forced the generals into making highly unlikely to succeed, again contributing to a lack of breakthroughs and a stalemate lasting for nearly 4 years.
Finally, the size of armies had expanded massively compared to even 50 years before. For example, during the 1870-71 Franco-Prussian War, Prussia and the other German states it was allied with put an army of 250,000 men into the field. In August 1914 some 4 million Germans were involved in the initial attack on France and Belgium.
Other armies were of comparable size, so there was no problem manning the entire trench system with troops.Further, even heavy casualties sustained on a regular basis in no way diminished the capability of the armies on both sides from keeping the necessary numbers of troops in the trenches to defend them effectively.
Thus, with neither side likely to run out of men any time soon,even attrition was unlikely to break the deadlock.With aged army commanders comfortably ensconced in chateaux and country estates miles behind the front, with no idea and less conscience about the reality of the type of warfare they were conducting, there was again little chance of the stalemate being broken.
So, for the reasons mentioned above - extensive defensive trench systems, modern weapons,and armies numbering in the millions - a stalemate quickly developed on the Western Front from the end of 1914.