The primary cause of the split between Sunni and Shia Islam centers around the question of who should lead the Muslim community after the death of the Prophet Muhammad in 632 CE. While Sunnis believe that the leader (Caliph) should be chosen from among the community, typically based on consensus or election, Shia Muslims believe that leadership should stay within the Prophet's family, specifically appointing his cousin and son-in-law, Ali, as his rightful successor. This fundamental disagreement over leadership and authority has led to distinct religious beliefs, practices, and political structures within the two branches of Islam.
The other options mentioned, such as the role of Muhammad as a prophet, the teachings in the Qur'an, and methods of spreading Islam, are important considerations in the broader context of Islamic history but are not the main cause of the Sunni-Shia split.