Gauss's Disquitiones Arithmeticae centers around the quadratic reciprocity law. It seems that he developed the genus theory of integral binary quadratic forms to find a natural proof of the quadratic reciprocity law. He later wrote 5 papers on number theory. All of them are about the quadratic and biquadratic reciprocity laws. Why did Gauss think the reciprocity law so important in number theory?
It's the first non-trivial result in elementary number theory, and to find out whether a second-degree equation has a solution modulo some number, basically comes down to knowing quadratic reciprocity. The Disquisitiones starts with the basic definition of congruences, then solutions of first-degree congruence equations, and then second-degree, where one naturally bumps up against this problem.
Here is from the book itself:
Later on he speaks of how Euler and Legendre came close to finding a proof, but despite their best efforts, could not. Clearly it was also a matter of pride for him.
Given how much of modern number theory revolves around generalizations of quadratic reciprocity, such as Artin reciprocity and the reciprocity conjecture of Langlands, it's easy to consider Gauss's intuition as justified.