Which is a major argument between Sunni and Shia muslims

These people were not agreeing with the successor, after the prophet Muhammad died the people wanted a different person, someone related, while other people wanted someone not related, people weren't agreeing with the successor that they wanted.

A major source of argument between Sunni and Shia Muslims is who is the rightful leader of Islam. This leads back to Islamic history, where Shia's believed that the son in law of the Prophet should have rightful accession to gain the Prophet's position after the Prophet died and to continue to lead the Islamic community. Sunni's do not believe that this should be an inherited position. The two communities have lived relatively peacefully until recent years where tension has risen.