Anarchy and Social Revolution
The key theme of the movie is social revolution and the ensuing anarchy that it causes. Because of social revolution, the principles of anarchy were implemented throughout Spain and lasted almost three years. The economy of Spain was put under the control of the workers and agrarian areas became collectivized and run as communes in direct opposition to the wishes and the dictates of the Communists who were also busy trying to wipe out fascism.
Semantics
All of the characters in the movie are opposed to fascism, and so it would be logical to assume that they were all on the same side, but in reality, the semantics of their ideologies separate them. In one scene, David is guarding the Communist Party headquarters in Barcelona and starts bantering with the anarchists across the barricades from him. He asks a fellow Englishman why he isn't standing alongside him, and the man asks him the same question in return. David replies that he really doesn't know. The men are separated by the dislike that their leaders have for each other. Each of the anti-fascist left wing organizations has its own specific objectives and ideologies and for that reason they are unable to come together instead allowing the semantics of their ideologies to prevent them from uniting as a single force.
