Major, when he addresses the group of animals that have met together at the beginning of the story, clearly is going to tell them something momentous, as he starts his speech by saying this will be his legacy as he feels he is about to die soon. He goes on to sketch out the grim existence that an animal can hope to enjoy in this life, especially given the way that they are worked so hard and fed only enough to be able to do that work. Finally, he points towards the major problem behind this condition, which is made all the worse because of the bounty that surrounds them: man. Note what he says:
Why then do we continue in this miserable condition? Because nearly the whole of the produce of our labour is stolen from us by human beings. There, comrades, is the answer to all our problems. It is summed up in one single word--Man. Man is the only real enemy we have. Remove Man from the scene, and the root cause of hunger and overwork is abolished for ever.
The biggest problem faced by the animals therefore is Man, because it is Man who enslaves them and uses them and takes the fruit of their labours away from them.