It was a very coordinated effort by Nikita Khrushchev after the death of Stalin. Khrushchev felt that the cult of personality hurt the Communist Party and the Soviet Union. The main thrust was done during a "Secret Speech" to the CPSU in 1956.

After Stalin’s death, the Central Committee began to implement a policy of explaining concisely and consistently that it is impermissible and foreign to the spirit of Marxism-Leninism to elevate one person, to transform him into a superman possessing supernatural characteristics, akin to those of a god. Such a man supposedly knows everything, sees everything, thinks for everyone, can do anything, is infallible in his behavior.

Additionally the reasons Khrushchev gave for the change.

Because not all as yet realize fully the practical consequences resulting from the cult of the individual, [or] the great harm caused by violation of the principle of collective Party direction and by the accumulation of immense and limitless power in the hands of one person, the Central Committee considers it absolutely necessary to make material pertaining to this matter available to the 20th Congress of the Communist Party of the Soviet Union.

Allow me first of all to remind you how severely the classics of Marxism-Leninism denounced every manifestation of the cult of the individual. In a letter to the German political worker Wilhelm Bloss, [Karl] Marx stated: “From my antipathy to any cult of the individual, I never made public during the existence of the [1st] International the numerous addresses from various countries which recognized my merits and which annoyed me. I did not even reply to them, except sometimes to rebuke their authors. [Fredrich] Engels and I first joined the secret society of Communists on the condition that everything making for superstitious worship of authority would be deleted from its statute. [Ferdinand] Lassalle subsequently did quite the opposite.

It is important to also realize that the General Committee, the ruling body of the Politburo and the Soviet Union (as a whole) knew exactly what the detriments were with the Cult of Personality and regarding Stalin. Majority of the Committee was executed during the Great Purges only 20 years prior. Stalin wielded complete authority and the General Committee was taking its power back after Stalin's death, leading to a weakened Khrushchev, comparatively.

It was also a maturing of the Soviet government. A more political machine than the governments before it. A sense of legitimacy now existed and the turbulent times was seen to be over. There existed a political power more so than a single man.