Why did the shiites break away from the rest of the Muslim community?

The question's phrasing implies that the "Rest of the Islamic Community" was maintaining a status quo and the Shiites diverted from this, but this is incorrect. Sunnis and Shiites came apart over how political power should be vested after Muhammad's death. As a result, both the Sunnis and the Shiites were formed by the disagreement.

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.)

The rest of the Muslim community broke away from Shiites. and the reason was power.