First of all, you have to realize that the US taking sole control of Korea would've been absurd, given how far away the US is and the geographical proximity to the Soviet Union. The question is why the Soviets were willing to split Korea. To which the answer basically is, they initially didn't care all that much about Korea. Neither did the US. (until they did). They cared about Japan, which was seen by both sides as the important strategical location in Asia.

So, the Koreans desperately were after independence and their own national state but, while the Soviets were at least somewhat sympathetic, it wasn't a very important matter to them. So when the US made an offer for a 20-30 year administrative split of Korea, they Soviets agreed (a split which would, of course, have impact to this day). It seems to be debated in the literature if this offer by the US was a first attempt by the US to fight for control in Korea or just another mindless decision made by the B-team of the military command that was assigned to Korea and was wholly ignorant of it's cultural and historical context (they at one point tried to get the old Imperial Japanese government to take over the administration of Korea - ouch!, talk about a cultural-historic faux pas!)

Whatever the motivations by the US ultimately were, Stalin agreed because at the time he was on fairly good terms with Roosevelt and saw no reason to be suspicious and thought that being forthcoming in the Korea matter would give him a better status in regards to Japan. Had he known what would follow he of course obviously would have decided differently but at the time Korea just wasn't seen as a geopolitical hotspot by the allies, it was fairly uncontroversial. The status of the joint allied administrative status of Korea was then officially anounced at the conference of Moscow in 1946, to massive protests of the Korean population, which felt betrayed by the allies since they had hoped for an immediate national independence after the abolishment of the Japanese Imperial Government.