Masechet Eduyot, Perek Aleph (Chapter One), Mishnah Dalet. In this Mishnah, we'll elaborate more on the previous Mishnah, where we had a Machloket (dispute) between Shammai and Hillel, and the Hachamim (Sages) end up giving an alternative answer, and Shammai and Hillel end up agreeing with the opinion of the Hachamim.
So the Mishnah asks: If we see that Hillel and Shammai both took back their original views once we have Hachamim received testimony that was authentic from the two weavers, the question becomes: Why do we even mention the opinion of Shammai and Hillel? If they ended up retracting quickly, why don't we just go with the opinion of the Hachamim? And that's all we'd have.
The Mishnah answers: It's to teach a lesson, to teach future people down the line that if a person has the ability to be modeh al ha'emet, to admit the truth, he should not stand stubbornly with the opinion that he had if the evidence is against him, if he's obviously wrong. The fathers of the world, Shammai and Hillel, the greatest people in the world, they were like the Avot (Patriarchs); they were like Avraham, Yitzchak, Yaakov. Even these people didn't stand by their opinions once they heard a decision a different way. So it's a lesson for the future of a people. Once you hear facts that go against the narrative that you have, it's time to just change. It's not about you being right; it's about finding the emet.