I hear from the Sfas Emes that if Moshe's sin would have been plain and simple he never would have done it. So it's not simple- it's very delicate. So you have many different versions what the sin was. So what's the story? Is only one rabbi right, or is it all Eylu ve Eylu?
To figure this out you must learn the Rashi in Ksuvos 57a, where he explains that if a rabbi says a Svora then even if the Svora does not make sense here, it can always be used in a different place where it would apply better, so you say Eylu ve Eylu. But if one rabbi says "the Rebbe said 'yes', and the other Rabbi says "the Rebbe said 'no', one of them is lying.
We like to say Eylu ve Eylu whenever possible because G-d specifically wanted that the oral Torah should be transmitted and FILTERED through the rabbis. (This is a whole subject in itself) And if you don't respect the Rabbis, the punishment is severe (Eruvin 21b) (They dump you into a boiling hot cesspool). (Click Jun 18, 2012)