I think you left out a point. Not just Nevua and Sanhedrin. The Gemara says Kishenismaatu Liban and Kishelo Shimshu Kal Tzarchan, is when Machlokes began. The Rambam learns that when a Talmid properly understands his Rebbe, his attitude and his take on a situation would be exactly like that of his Rebbe.
Once they weren’t Mekabel fully to this degree their view has a flavor of their own. This breeds Machlokes, since each Talmid has his own view and they are not reflecting the one view they recieved together.