This is a good question. The book does not explicitly say why the pigs had the leadership roles of teaching and organizing. However, if we look at the book, it is pretty clear why they served these roles.
First, it must be said that the pigs were not given these roles. They took these roles. This is an important clarification.
Second, there might have been some continuity between Old Major, being a boar, and the pigs. In other words, leadership from boar to pig might have been natural.
Third, more importantly, the most intelligent of the animals were the pigs. They knew how to read and communicate effectively. Here is what it says:
The pigs now revealed that during the past three months they had taught themselves to read and write from an old spelling book which had belonged to Mr. Jones’s children and which had been thrown on the rubbish heap.
This fact alone made them into leaders.
Finally, Napoleon took greater initiative to lead and organize. He had great foresight, such as when he nurtured the dogs. Later he would use them as guard dogs.