I know that Stalin was concerned about the future security of the USSR. After all, the USSR lost almost 20 million people. However, the USSR was communist and didn't Roosevelt and Churchill want to stop the spread of communism?
They agreed to do it in part because they had no other choice. It was already, de facto, in the Soviet sphere of influence. The question was whether they could convince the Soviets to relent a bit on what that might mean. So they thought that Stalin might actually let Poland be democratic, which turned out to be false.
This is a map of the front as of around February 1945, when Yalta took place. You can see that the Soviets already have most of Eastern Europe under their control. The parts they don't have will be in their grasp sooner than they will be in anyone else's grasps. These were the military "facts on the ground" and to imagine anything else happening in the postwar, you have to imagine that the Soviets could be convinced to relinquish that acquired control. Diplomatically they assessed that was mostly out of the question except maybe in terms of Poland. And they did not care enough about Eastern Europe enough to try to force them to relinquish that control militarily.
On this matter, Michael Dobbs' Six Months in 1945: From World War to Cold War is instructive, as he is relentless in emphasizing the importance of the "facts on the ground" about this sort of thing. It is one of the ironies of WWII that it gave the USSR an excuse to invade a huge number of countries in the excuse of "liberation" from the Nazis.
/u/restricteddata has ignored other reasons why Roosevelt agreed to the Soviet sphere, even if the reason he provided is paramount. Roosevelt wanted the Soviet Union to help defeat Japan after the war in Europe ended, and he wanted Stalin to help him to maintain the United Nations after World War II. He couldn't very well challenge Stalin on Eastern Europe and realize either of these other goals. Furthermore, Roosevelt simply did not care for Eastern Europe the same way he did Western Europe. It is unimaginable that Roosevelt would have been so accommodating if Stalin sought to incorporate France, Belgium, or his own ancestral grounds the Netherlands, no matter what the "facts on the ground" might have been.
