Avos, Chapter 4, Mishnah 15 - in many editions of the Mishnayos it appears as Mishnah 12. In this mishnah we meet Rabbi Elazar ben Shamua.
Rabbi Elazar ben Shamua is the "Rabbi Elazar" mentioned throughout the Talmud and the Mishnayos: wherever Rabbi Elazar is mentioned without his father's name, this is the one intended. Rabbi Elazar was one of the five later, central students of Rabbi Akiva, the students who rebuilt the world of Torah, and he was one of the five who received semichah from Yehudah ben Bava at the close of the Hadrianic decrees.
A particularly important point: Rabbi Elazar was the teacher of Rabbi Yehudah HaNasi, the compiler of the Mishnah. As a child Rabbi Yehudah HaNasi learned from his father, and afterward from Rabbi Yehudah bar Ilai, and later he turned to Rabbi Elazar, who was apparently the greatest man of that generation. There are mishnayos and statements of Chazal that support the idea that he was indeed the greatest of all of Rabbi Akiva's students. Hence Rabbi Elazar's important place in the chain of the mesorah.
The foundation of the mishnah:
There are various relationships that call for a certain measure of reverence and honor. Giving honor to another person requires submission, and at times even setting oneself aside before him, and that is why it is difficult: a person has an ego, and therefore he is liable to fall short of his obligations. The mishnah therefore aims high - to strive for the maximum measure of honor and reverence, so that at the very least what one is obligated to give will indeed be given.
"Yehi kevod talmidcha chaviv alecha keshelach":
The honor and esteem given to one's students should matter to a person as much as his own honor. A person's own honor certainly matters to him, and so he should not give his students any less than that.
Why do students deserve honor? After all, they are his students, subordinate to him.
The answer lies in the well known statement of Chazal:
"Harbeh Torah lamaditi merabosai" - much Torah a person has learned from his teachers.
"Umechaverai yoser mehem" - from his colleagues he learned more than from his teachers.
"Umitalmidai yoser mikulan" - and from his students he learned more than from all of them.
This is an extremely important principle. A teacher must understand that he needs his students, because the very nature of students is to ask questions, to poke holes and to serve as a sounding board. When a student does not understand, it is not the student's responsibility to understand, but the teacher's responsibility to clarify. The students' questions allow the teacher to verify that the material is clear to him, and they alert him to what he has not properly grasped. It emerges that students are an essential component in a teacher's path toward genuine mastery of his own Torah, and for that reason they deserve honor no less than a person's own honor.
This principle is supported by a verse in Shemos: when Moshe Rabbeinu spoke with Yehoshua he said to him, "Bechar lanu anashim vetzei hilachem baAmalek" - "Choose men for us and go out and fight Amalek." The word "for us" teaches that Moshe Rabbeinu placed Yehoshua, his student, on equal footing with himself.
"V'chvod chavercha k'mora rabbach":
The obligation to give honor applies to every person, and certainly to a friend; the obligation of awe, of reverence, applies only to one's teacher. The Mishnah comes to teach that the honor a person gives his friend should not fall short of the awe he feels toward his teacher; rather, he must raise it to that very level.
In this there is a recognition of the irreplaceable importance and value of friends, as the saying goes, "either companionship or death." A person needs a friend in order to get through life:
To support him and to tell him what is right and what is not.
To rebuke him when he is in need of rebuke.
To serve as a sounding board for him.
To give him the emotional support he needs.
Therefore one must never make light of the honor and the seriousness that a friend deserves.
"U'mora rabbach k'mora Shamayim":
A person's awe and reverence toward his teacher and master should be like his awe of Heaven, of the Holy One, blessed be He. This principle is based on the verse that obligates fear of Heaven, which includes fear of Torah scholars as well: "Es Hashem Elokecha tira" - you shall fear Hashem your God; the word "es" comes to include Torah scholars. It emerges that the obligation to revere one's teacher, a Torah scholar, is bound up with the obligation to revere Hashem and is almost equal to it.