I understand both the military leaders really wanted to win, but why is it, that with so many people dying for literally nothing, they didn't withdraw the army for four years?

This sounds a bit like Trotsky's solution of "neither war nor peace" to the war on the Eastern Front in 1918, where he declared that Russia was unilaterally withdrawing from the war with Germany, peace treaty or no. The German response to this piece of diplomatic genius was to advance 150 miles in a week and force the Russians to accept a much harsher peace treaty at Brest-Litovsk. Had the Germans offered that solution to the British and French on the Western Front, it would have been tantamount to offering a white peace and withdrawing back to pre-war borders, an offer that would not have been acceptable to the Western Allies given that Germany had invaded them. Had the French offered that solution, it would have been tantamount to giving up Paris and offering an unconditional surrender.

I think this question boils down to, "Why did the British and French continue to attack on the Western Front in the face of minimal gains for extremely heavy casualties?" The answer to that question is quite simply that France had been invaded. Its sovereign territory had been occupied by an aggressive power. In the face of that, sitting still was not an option. In 1914, France lost 64 percent of its pig iron production, 24 percent of its steel manufacturing, and 40 percent of its coal industry behind German lines, to say nothing of 2 million French citizens. Had a French General got in touch with his German counterpart and offered to end the war in those circumstances, the German response would have been an emphatic "Yes please!" The French government's response would have been to sack him, probably denounce him as a traitor, and replace him with another General who was not manifestly insane. Particularly in the democracies of Britain and France, Generals were responsible to democratically-elected governments who had the final say on whether the war continued or not.

In hindsight, and assuming that strategy takes place in a vacuum, one could say that the best strategy that Britain and France could have adopted in the West would have been to remain on the defensive and wait for the Royal Navy blockade to starve Germany to death. In reality, however, strategy is subject to politics, and such a strategy would have been politically-unacceptable both to the French government, and to the French people, who had seen their country invaded and occupied. While alternative strategies were considered (see Churchill's obsession with "soft underbellies", or the "Easterners" in the British Cabinet who would have preferred to focus on Imperial defence by dismantling the Ottoman Empire), none of these would have defeated the centre of gravity of the Central Powers: the German Army on the Western Front. And the only way to defeat it was to prize it out of its positions in France and Belgium by means of offensives, whether by aiming for a breakthrough, or, as ultimately happened, by attriting it to death.

Sources:

Gordon Corrigan, Mud, Blood and Poppycock

Robert Gerwarth, The Vanquished: Why the First World War Failed to End, 1917-1923

Peter Simkins, et al., The First World War: The War to End All Wars

Gary Sheffield, The Chief: Douglas Haig and the British Army

Dennis Showalter, Instrument of War: The German Army 1914–18

Matthias Strohn, et al., 1918: Winning the War, Losing the War