How and why is Animal Farm an unrealistic story?

Animal Farm is an unrealistic story because it is about animals that plan and execute a revolutionary rebellion against their human owners/rulers.  

It is also unrealistic because it has animals forming a governing ideology called "Animalism."  It's a lot like communism, which is real, but animals forming a society based on an ideology and drafting commandments to live by is definitely what I would call unrealistic.  

The story continues its unrealistic characteristics by having the animals talk to each other, gesture, and express human emotions.  They plan to build windmills and other forms of infrastructure too.  

It's also unrealistic for pigs to begin walking on two feet and wearing clothes like humans.  

The story is not meant to be taken at a literal level though.  Animal Farm is an allegorical commentary on the communism that was happening in Russia.  One thing that an allegory will do is take specific characters or situations and have them stand in for other characters or situations in order to make a point about them.  That's what Animal Farm is doing, and the point it's making about communism is not a glowing endorsement of that system of government.