Answer:
In his autobiography, Malcolm X said that one of the reasons for the breakdown was the growing tension between him and Elijah Muhammad due to his dismay at Muhammad's rumors of extramarital affairs with young secretaries. These actions went against the teachings of the Nation. Although Malcolm initially ignored the rumors, he spoke with Muhammad's son and the women who made the accusations. He came to believe that it was true and Muhammad himself confirmed the rumors in 1963. Muhammad tried to justify his actions, referring to the precedents of the biblical prophets.
Another reason was envy, since Malcolm X had become the favorite of the media, and many at the Nation headquarters in Chicago felt that it overshadowed Muhammad. Louis Lomax's book on the Nation of Islam in 1963, entitled When the word was given, included a picture of Malcolm X on the cover and five of his speeches, but only one of Muhammad, which greatly annoyed him. Muhammad was also jealous because the editor was interested in the autobiography of Malcolm X.
Even so, formally, at the moment of its rupture, Malcolm X explained that he was leaving the Nation of Islam due to its doctrinal rigidity.