The erudite were against abnegation leadership. what was the most important reason

The reason is they doesn't believe with Abnegation's logic. They want to instill and strengthen the faction system.  

Abnegation is a faction that values selflessness, kindness and helping other people regardless of factions and even they are factionless. Some of them became public servant out of their love for others. Their color symbol is gray. Most of the leaders in Divergent book are from this faction as they have a value for others.

Erudite is known for being intelligent and logical people. They are normally dressed in blue clothes and wearing glasses to make themselves look smarter. They value knowledge and logic very much that they doesn't agree to ignorance and other negative thoughts that are natural in the human mind. In the Divergent book, erudites become too smart and they became obsessed with knowledge that they form a revolution against the government to make themselves leaders of the whole city and take over. They formed an alliance with Dauntless, the fierce and brave faction to kill Abnegation leaders. With this Erudite's nature, it was the total opposite of Abnegation.  

The important reason here in real life is : heart (kindness, generosity and selflessness) is cannot get along with the brain (logic, knowledge and skills). They are always contradicting and doesn't work well in most cases of our lives.

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