Clearly, what concerns the rabbis when it comes to factionalism is the possibility of Jews disagreeing about the Law in public. No wonder even the greatest sages hesitated to get involved in disputes between the two schools. “They asked Rabbi Yehoshua: What is the law with regard to the rival wife of a daughter? He said to them: It is a matter of dispute between Beit Shammai and Beit Hillel.” But this evasive answer wasn’t enough to satisfy the questioners, who pressed him: “And in accordance with whose statement is the law? He said to them: Why are you inserting my head between two great mountains?” Getting caught between Hillel and Shammai was like being caught in a war between mountains—or, as we might say, between rock and a hard place. No wonder it took a divine voice to settle the argument between them.
Earlier Daf Yomi columns are noted here and links.