1- The mistake that led to the eigel was thinking Moshe had inherent qedushah, and therefore they needed an an inherently holy eiegel to replace him. Therefore, Moshe breaks the luchos, carved and written by G-d, forcefully demonstrating that even they don’t have inherent qedushah.

2- The luchos could be read from two sides just as Hashem’s Existence can be read from two sides — from nature outward, or from the Torah inward.