Why did the disputes over authority after Muhammad's death hinder future Muslim unity?
I do not know what Chapter 6 of your book says, but I would say that the answer to this is that the disputes over authority after the death of the Prophet Muhammad led to the split between Sunni and Shia Muslims.
After the death of Muhammad, one group of his followers felt that there should be an election to designate his successor. This group chose Abu Bakr and they would later become the Sunni.
Another group of Muhammad's followers believed that only God could pick a successor to Muhammad. They believed that Ali, Muhammad's son-in-law and cousin, was chosen by God. This group became the Shia.