The main development that leads to the expulsion of Snowball from the farm is his conflict with Napoleon. At first all seems well, but as the story progresses, Snowball grows in power. For example, he is a commemorated war hero, and he proves to be a better speaker (as well as the more intelligent one). He is also forward thinking as he wants to build a windmill to provide electricity for all the animals. A windmill can automatize things and so make life easier and more efficient.
Napoleon obviously does not like the new attention given to Snowball. He is jealous. Instead of a windmill, Napoleon believes that the animals should focus on their current task, which is to run the farm and grow food. So, when Snowball makes these suggestions, he disagrees, and all the while he is plotting an overthrow. He gains the support of the dog, and when the time is ripe, he gets the dogs to attack Snowball and drives him out.
The major event that leads to Snowball getting thrown off the farm is when Snowball gives a speech about the windmill. He is calling for the animals to vote for building the windmill.
Napoleon does not want the windmill to be built. Instead, he wants the animals to concentrate on growing food. Because of that, he has his dogs chase Snowball off the farm.
There are a couple other things that lead to Snowball getting expelled. First, he has become a hero and that threatens Napoleon. Second, he has also disagreed with Napoleon about the best way to defend the farm from outside attacks.
Well Napoleon thought that Snowball was threatning his position as leader so he quickly got rid of him. The lust of absolute power also contributed to Snowball's Expulsion. It is clear that Napoleon always disagreed with Snowball even though he knew what he was doing was right. This tells us that while Snowball served the farm Napoleon only served himself