Why do Sunnis and Shiites have differences of opinion?

Answer 1

It is unclear what the question means by "differences of opinion".

It is not as if all Sunnis like Football Club Barcelona and all Shiites like Real Madrid and so they have a difference of opinion over which football team is better.

If you are referring to dogmatic differences, these are not differences of opinion, but differences of theology and politics. The disagreement came to a head when the two groups were discussing who should be the Successor after Mohammed's death.

The Muslim community was united while Mohammed was the leader of this community. Most Muslims hold, however, that he never specifically chose a successor to his leadership. There was a minority in the community that supported the candidacy of 'Ali, the Prophet's son-in-law, this political faction became known as the "Supporters of 'Ali" which in Arabic is Shiat 'Ali (where the modern term "Shiite" comes from). They derived their support from specific hadiths and events that they claimed showed that God had revealed to Mohammed that 'Ali would succeed him. The majority of Muslims held that these hadiths and events showed nothing more than that 'Ali was very pious, something they did not deny. Therefore they gave power to the man who was Mohammed's second-in-command and father-in-law Abu Bakr. This majority were called the People of the Customs [of the Prophet] which in Arabic is Ahl Sunna (from where the modern term "Sunni" comes from.)

It is important to note that the split between the Sunnis and the Shiites was not the only split in Islam. There were numerous other theological splits such as the offshoots of the Kharijites, the Mu'atazilites, the Baha'i, the Druze, the Ahmadis, and other groups. The difference is that these offshoots are <1% of the total Muslim or quasi-Muslim population and therefore not often discussed.