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Because the movement was set up (or very quickly taken over) by communists:
Pacifism has always found great resonance in communist thought and action from its origins. Thus, the Amsterdam Pleyel movement in the 1930s foreshadowed the postwar communist pacifist movement.
Partly from the French Resistance (the future French Peace Movement ), partly from the gathering of intellectuals against the atomic weapon (the future World Peace Council ), the Global Movement of Peace Supporters (generic expression global) will be rapidly controlled by the international communist movement ( Kominform).
I placed the relevant text in bold
This was a common tactic used by the Soviet Union if they couldn't militarily match their opponents.