The Talmud in מסכת גיטין discusses the concept of דרכי שלום, the need to establish rules that will increase peaceful relations in the Jewish community.
The Gemara's first example of דרכי שלום is that in the Beit Knesset, we must call to the Torah a Kohein first, followed by a Levi, followed by a Yisrael. The purpose of this rule is to avoid fights in the Synagogue.
The Talmud relates that Rav Ami and Rav Assi were both prominent Kohanim and they insisted that the great Rav Huna be given the first Aliya because he was clearly the greatest rabbi of the generation.
The Tosfot Rid points out that even when one is the spiritual leader of an entire city, he should not take the place of a Kohein. This is because of the jealousy factor and that there will inevitably be individuals that feel they are more learned and more qualified.
This is why the rabbis instituted a specific order of distributing honors in Shule, to maintain דרכי שלום.