The Wikipedia on Tannaim says this
Until the days of Hillel and Shammai (the last generation of the Zugot), there were few disagreements among Rabbinic scholars. After this period, though, the "House of Hillel" and the "House of Shammai" came to represent two distinct perspectives on Jewish law, and disagreements between the two schools of thought are found throughout the Mishnah.
But how did these initial disagreements arise? If we accept that there were few disagreements before then, then presumably for any issue they later disagreed on there was already a (single) currently established practice on the ground - one way or another. How could one side suddenly introduce a viewpoint that differed with that practice?
Why did these disagreements arise at that particular point in history and not earlier?