In numerous Halachic disputes I spotted two contradicting approaches:
"אלו ואלו דברי א' חיים" - both approaches are legitimate and stem from the [one] living G-d. Each one is allowed to keep his way and his Halochos without forcing others to accept.
"נעשית תורה כשתי תורות" - the two approaches appear as two different Torahs, therefore an obligating Halochoh must be issued for all.
How they can be reconciled?
(Understanding of this contradiction is especially useful for resolving my previous question about B"H and B"S wars: "what-happened-in-r-chananyas-penthouse-18-dvarim")
Examples (I'm not claiming "שתי תורות applies in every example, but it looks like it):
B"H and B"S war: It was OK to have both schools side by side (as או"א) for some time, but [suddenly] it became "שתי תורות" and had to be [brutaly] resolved.
R' Yehoshua and R' Gamliel on Kiddush Hachodesh: it was fine to have different schools until R"G decided to end it and rule himself.
R' Eliezer and Chachamim in Tanuro Shel Achnai: R"E had his approach standing for decades alongside Chachamim's and all of sudden he finds himself boycotted.