Why was Berlin divided after ww2 if it was inside east germany?

I haven't checked on previous answers here, but here is a quick summary:

Even before the end of the Second World War, the "big four" (US, UK, Soviet Union and France) had agreed on a partition of Germany into four allied zones; but since almost 30% of Germany's industry before the war had been based in Berlin, including some of its biggest companies (eg Siemens, AEG) and Berlin was therefore of not just highly symbolical value, it had been decided that, just as for Austria, the capital of Germany would have representations of all allied nations, and that therefore Berlin itself would be divided into four sectors. It was more a function of the geographical layout than anything else that dictated that the western allied sectors of Berlin would therefore be inside the Soviet future zone of Germany. And, since the Soviets made it to Berlin first and took it before Western troops got there, the western allies had little choice but to point at the previous agreement. The little section of the Soviet zone down south near Erfurt the Americans had liberated was handed "back" to the Soviets so that all zones and sectors could be set up as previously agreed.
The cold war was not as deeply set in everyone's mind at that point yet, and the allied assumption at this point was largely still that everything could be worked out once Nazi Germany had been properly defeated.
Future trouble was, however, not completely out of sight: the allies did agree that they guarantee each other's rights to access to their sectors of Berlin, which was the legal base on which the US, UK and France could shortly later (in 47/48, and again 61) operate the Berlin Airlift and the firm stance that the "West" (three Western sectors of Berlin) were to be freely accessible to them (and therefore to all Western civilian traffic as well). This would not have been part of the agreement if all sides had trusted each other completely.

Nevertheless -- and this is probably the most important legal part of the Berlin question -- West Berlin was not a part of West Germany. It remained formally a separate entity, legally under Western allied authority, and under nobody else's jurisdiction. West Germany had no rights or claims to West Berlin, other than its own (and Western allied accepted intrepretation) that only West Germany could be considered the future heir of all rights and responsibilities of a united Germany. Thus, West Berlin's elections had regular West German parties, and even members of parliament -- but these did not have formal voting rights in the West German parliament. They were, legally speaking, "visitors" there, but their votes were "respected" by the West German parliament as "opinion input" (which really was a necessary charade run for legal reasons).

So there was no intention to create a "spy paradise" in Berlin. It was all just the absurd outcome of the separation of the country into two ideologically opposed camps after the war, based on the technical complications deriving from the allied agreements before the end of the war.