From an earlier answer of mine

Berlin was an anomalous entity during the Cold War and its very status was reflective of a series of contradictions. West Berlin, for example, was not technically part of the FRG, even though it fell under Basic Law and could send non-voting delegates to the Bundestag. East Berlin was the de facto capital of the GDR, but there were many signifiers that stressed it was a divided and incomplete city. It was not until 1970 that East Berlin's official designation changed from "Democratic Sector of Berlin," to the more neutral "Berlin capital of the GDR." One component of the FRG's Hallstein Doctrine was to limit global recognition of East Berlin as a capital and for nations in the Third World to open up embassies in East Berlin courted a response from the FRG. For most of the Cold War, Berlin's status was in a simultaneous state of flux and paralysis; official declarations and policies claimed that the city's division was temporary while structures like the Berlin Wall told the opposite.

One of the major reasons for this odd state of affairs was that the status of Berlin was one of the first casualties of the breakdown in inter-Allied relations at the very beginning of the Cold War. Policymakers first floated the idea of Berlin division in a concrete manner after the Casablanca Conference in 1943, and later codified by the Protocol on Zones of Occupation and the Administration of "Greater Berlin" which set up three partition zones (France was initially excluded). Allied conferences at Yalta and later at Potsdam firmed up these agreements with the The Allied Governments on the Zones of Occupation and the Administration of "Greater Berlin" in July 1945. The understanding for these agreements was that the Berlin occupation, as well as the rest of the zonal occupations, were to be temporary affairs until a final peace treaty could be arranged between the Allied powers and an acceptable successor German government.

In theory, a proper German government would sanction the territorial adjustments to German territory made at Yalta and Potsdam, sign a proper peace treaty, and then govern over a unitary German state, presumably with Berlin as its capital.

Both Berlin and Vienna (which was also an divided exclave in the Soviet zone of Austria) were both administrative and political centers of Germany and Austria. The logic of the wartime agreements was that these divided capitals would be the nerve centers for inter-Allied cooperation. There was some effort put into developing the Kammergericht as an official meeting place for the Allied Control Council. This arrangement soon broke down and each occupation power found it much easier to govern their territory from their own occupation zone (Soviets in East Berlin, French in Karlsruhe, the Americans in Frankfurt am Main with a sizable presence in West Berlin, and the British in Bad Oeynhausen). American actions in West Berlin, such as opening the Free University, demonstrated that even as Berlin's political importance faded in light of Germany's imminent division, it still had symbolic importance. other aspects of the cultural Cold War saw the development of West Berlin as a means to undercut the Soviet claim to be the leader of Europe's reconstruction. The Amerika Haus in West Berlin was one of several well-funded centers for US public diplomacy, and was open to all Germans, as this 1948 German newsreel shows. But by 1948, actions like the creation of Bizonia the previous year, the provisional steps to draft a new German constitution, and the general walking away from wartime agreements by the Americans was a signal that Washington was sanctioning a permanent German split. The Soviets themselves were not entirely blameless in this matter, and elections in the Soviet zone clearly favored the SED and the zone was well on its way to forming its own state.

Stalin's general response to this exclave within the Soviet zone (soon to become the GDR) was that it was both an embarrassment and that Western Allies had to be pressured out of the area through a combination of hard and soft measures. The SED press, much of which was centered in Berlin, emphasized the importance of the city's unity and blamed division on the West. Likewise, the Soviets began to put the crews of transportation links to the city form the West, a move which culminated in the Berlin Blockade and Airlift. The immense propaganda success of the Airlift for the Americans overshadows that Stalin's strategy for Berlin was not as bad of a strategy as it might seem at first. Most American military opinion correctly felt that West Berlin's military garrison could at best fight a last stand if Soviet military forces moved against it. Nearly all military plans for West Berlin during the rest of the Cold War had an air of fatalism about them. Additionally, maintaining the exclave itself was an economic drain both for the Western powers and for any future West German government, and the long-term trajectory of the West Berlin economy bears this out. Bonn had to subsidize many West Berliners with what were derisively known as Zitterpramie (jitter bonuses), which became a burden as West Berlin's industry died out. Part of the reason why so many German student radicals gravitated to West Berlin was not just because they would be exempt from conscription or the student movement at the Free University, but because rents for rather large apartments were quite cheap.

There was a streak of pragmatic calculation in Stalin's treatment of Berlin and to an extent, he expected his Cold War foes to behave pragmatically as well. In an August 1948 meeting with the British and French ambassadors in middle of the Airlift, Stalin argued that the division of Berlin only made sense if the Allies were treating Germany as one country. Since it was clear by mid-1948 that the Western Allies were supporting the emerging West German state, Stalin told the ambassadors that it only made sense that they should abandon Berlin since its vulnerability meant it could never be a capital for such an entity.

But the decision to decision to maintain West Berlin was neither a military or practical one, but a political one. As such, the head of the US occupation General Lucius Clay argued firmly that Allied commitments to West Berlin needed to be honored. Clay's resolve helped stiffen the determination to continue the commitment to West Berlin back in policy corridors in Washington. Although Washington nixed Clay's suggestion for an armed land convoy, the Pentagon lent its support for an airlift (which Clay had already authorized) as a more neutral alternative.

This type of flexible response to West Berlin put the Soviets on the horns of a dilemma that would characterize its Berlin policy for the next two decades. Moscow had already made a commitment to a unified Berlin and blamed Western perfidy for the division of the city. But Soviets were never willing to risk open war with the West for this political position. So any pressure the Soviets or the GDR put on the city could be rendered null by any Western counterpressure as the Soviets never wished to escalate the crisis beyond measures that could lead to war. To adapt one of Bismarck's aphorisms, West Berlin was not worth the bones of a Ukrainian Ryadovoy. The exclave proved to be a consistent headache both for the Soviets and the GDR, especially in the 1950s when West Berlin was a conduit for GDR refugees, but so long as the West remained committed to West Berlin, neither the Soviets nor the SED had the political wherewithal to force them out. The Berlin Wall exemplified this problem. The Wall was not so much designed to keep the West out, despite its official designation as an "anti-fascist barrier," but to keep East Germans inside the GDR by denying them an easy egress.

What this meant was the division of Berlin remained like an appendix to a German problem that had evolved into a different animal than it was in 1944/45. Allied agreements remained in force over Berlin long after both Germanys had assumed all the trappings of a sovereign state. The Quadripartite Agreement on Berlin in September 1971 recapitulated large parts of earlier agreements, but also confirmed various transportation agreements, suggesting that both sides of the Iron Curtain saw Berlin's division as temporary affair that would remain the status quo for the foreseeable future. Ironically, the Cold War situation of "permanent transience" over Berlin and German division greased the wheels of German unification in 1990. The contours of the postwar agreement were already known, and they gave the Kohl government an advantage to push for a final peace treaty that sanctioned German unification by the Allied powers of 1945, the 2+4 Treaty, signed in September 1990.