Doros Harishonim (vol. 1 p. 200) traces it to the appointment of the Hellenist Yosef ben Toviah as chief tax collector of Eretz Yisrael (Josephus, Antiquities 12:4:2ff), and the resulting growth of the Hellenists as a force. Up to that point the Kohen Gadol had been responsible for internal and external governmental affairs, including collecting taxes on behalf of the ruling power. But now that he had abdicated that responsibility to ben Toviah and his cronies, the Sages found it necessary to create a new position, from within the Torah leadership, to assume those functions.
To quote R' Avigdor Miller zt"l's paraphrase (Torah Nation, par. 246):
Because of the disturbed conditions, the Sanhedrin now took the step of instituting the new office of Nasi. They had seen how the Cohen Gadol had allowed his impious nephew to gain power in the land, and they feared that he could no longer be entrusted with the authority which had hitherto been invested in the high-priesthood. They therefore now decided to transfer to a Nasi those duties which had formerly been discharged by the Cohen Gadol but which were now being neglected because of the deterioration of that office. In addition to the Av Beth-Din, the Nasi would be chosen from the Sanhedrin of the Sages; he was to be the supreme leader of the Torah-Sages of Israel, and he would be the Torah-spokesman who addressed himself to the nation and to the outside world.
(Not sure where you're getting "1500 years," by the way. From Matan Torah until the first of the Zugos was about 1100 years. Also, the first four of the Zugos did argue about one issue - semichah on Yom Tov (Chagigah 16a).)
As for its being abolished - it wasn't, necessarily; we still have a Nasi and Av Beis Din in later times (for example, Rabban Gamliel II and R' Yehoshua, and Rabban Shimon ben Gamliel II and R' Nosson). That they're not called "Zugos" might be because from those periods we have many other Sages quoted by name, and indeed some of them (like R' Akiva) are considered links in the chain of mesorah even though he was neither a Nasi nor an Av Beis Din.