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.