To understand the basis of the conflict between the Tzedukkim and the Perushim, a conflict which is referred to in the Talmud and the writings of the Jewish historian Josephus, one must summarize the history of the priesthood of Israel from its beginnings to the rise of the Hasmonean Family to that position.
According to the narratives and the laws of the Torah, Aaron, the brother of Moses was the first of the Kohanim. The Kohanim thereafter were to be the descendants of Aaron. Thus, Aaron, at his death, was succeeded by his son El'azar, who was succeded by his son Pinchos. All the descendants of Aaron were Kohanim and the Jews of our time who are Kohanim are direct descendants of Moses' brother Aaron, the first of the Kohanim of Israel. Of course, only one man could serve as Kohen Gadol. His brothers and all of their descendants in the male line were also Kohanim, but only one could serve in the supreme position.
When David was King of Israel the High Priest was Eviosor. But after David's death there was a struggle for the royal succession. His two sons, Adoniyahu, the son of Hagith and Solomon, the son of Bat-Sheva were rivals for the throne, and people of power and influence were divided in their loyalties. Ebiosor the High Priest favored the candidacy of Adoniyahu and Zadok, another priest who had risen in the hierarchy, was a partisan of Solomon. Nathan the Prophet supported Bat-Sheva's claim and was in favor of Solomon. We know how the struggle ended. Solomon was chosen king, was annointed and crowned
When Solomon became King of Israel, he named Zadok as High Priest and dismissed Eviosor, ordering him to leave Jerusalem and to retire to his family estate in the town of Anatoth, which is some 17 kilometers northeast of Jerusalem. Thus the family of Ebiathar remained in Anatot, known as Kohnaim and continuing the tradition of being Kohanim, but without serving in any capacity in the Temple in Jerusalem. One of the Kohanim of Anatot was the prophet Jeremiah, perhaps one of the greatest spiritual personalities in Israel's history. But he never served in a priestly capacity.