Berlin was a flashpoint in the Cold War largely because it was the place where it was easiest for people to move from the communist bloc to the West. East Germans could very easily go to West Berlin and declare themselves refugees, thus gaining the ability to go to other parts of West Germany. It is said that about 3 million East Germans did this.
The refugee problem was very acute for East Germany. It could not afford to keep losing that many young and educated people if it wanted to have a decent economy. Therefore, there was a great deal of pressure put on the Russians by the East Germans to close the border or to take West Berlin.
Khrushchev proposed a demilitarized Berlin. This was not acceptable to the Allies since West Berlin would be isolated and defenseless in the middle of East Germany. This led to serious tensions until the Berlin Wall was built.