Stephen I. Ternyik The following story can be found in the Eruvin 13b: For three years, the House of Hillel and the House of Shammai argued. One said, 'The halakha is like us,' and the other said, 'The halakha is like us.'
A heavenly voice spoke: "These and these are the words of the living God, and the halakha is like the House of Hillel."
A question was raised: Since the heavenly voice declared: "Both these and those are the words of the Living God," why was the halacha established to follow the opinion of Hillel?
It is because the students of Hillel were kind and gracious. They taught their own ideas as well as the ideas from the students of Shammai. Not only for this reason, but they went so far as to teach Shammai's opinions first.
Because if you care about the truth you will also accept the truth from your opponent and accept it as a truth from God and not just dismiss it because it came from your opponent. Furthermore a certain inner quality is needed: Kindness and gracious which also reflect certain qualities of God. But also the right wisdom to put certain ideas in the right place (they tought the opinion of Shammai first, because it was necessary in order to understand their teaching). Putting things in the right order und being able to make further developments is what enabled them.
So obviously at some point and after 3 years they were able to reach that point, to see that they are both right and how it fits.