Paul seems to be being being sarcastic (but please either read to or skip to the section break as I have a different view).
Paul considers αἱρέσεις/αἱρετικός to be a horrible thing:
Tit 3:10 Have nothing to do with a divisive person [αἱρετικός]
after you have warned him once or twice. Tit 3:11 For you know that
a person like this is corrupt and keeps on sinning, being
self-condemned.
- the occasion of 1 Corinthians and its prevailing theme is Paul addressing the terrible news that this assembly has in short order devolved into cliques and sects (αἱρέσεις):
1Co 1:10 I appeal to you, brothers, by the name of our Lord Jesus
Christ, that all of you agree, and that there be no divisions among
you, but that you be united in the same mind and the same judgment.
- he does not criticize the teaching of any of the distinguished teachers (in fact he praises them) but roundly denounces identification with any teacher other than the Christ:
1Co 1:11 For it has been reported to me by Chloe's people that there
is quarreling among you, my brothers. 1Co 1:12 What I mean is that
each one of you says, "I follow Paul," or "I follow Apollos," or "I
follow Cephas," or "I follow Christ." 1Co 1:13 Is Christ divided?
Was Paul crucified for you? Or were you baptized in the name of Paul?
1Co 1:10 I appeal to you, brothers, by the name of our Lord Jesus
Christ, that all of you agree, and that there be no divisions among
you, but that you be united in the same mind and the same judgment.
There are two main historic ways that assemblies have dealt with differences of opinion:
by creating authoritative dogmas (Popes, creeds, councils, statements of faith, etc.)
by dividing into sects/denominations
In Corinthians Paul provides the better approach (aka "more excellent way") which involves taking turns teaching while the others listen:
1Co 14:26 What is it [the better approach] then, brethren? whenever
ye come together, each of you has a psalm, has a teaching, has a
tongue, has a revelation, has an interpretation. Let all things be
done to edification. 1Co 14:27 If any one speak with a tongue, let
it be two, or at the most three, and separately, and let one
interpret; 1Co 14:28 but if there be no interpreter, let him be
silent in the assembly, and let him speak to himself and to God. 1Co
14:29 And let two or three prophets speak, and let the others judge.
1Co 14:30 But if there be a revelation to another sitting there , let
the first be silent. 1Co 14:31 For ye can all prophesy one by one,
that all may learn and all be encouraged. 1Co 14:32 And spirits of
prophets are subject to prophets. 1Co 14:33 For God is not a God of
disorder but of peace, as in all the assemblies of the saints.
1Co 14:36 What? came the word of God out from you? or came it unto
you only? 1Co 14:37 If any man think himself to be a prophet, or
spiritual, let him acknowledge that the things that I write unto you
are the commandments of the Lord. 1Co 14:38 But if any man be
ignorant, let him be ignorant. 1Co 14:39 Wherefore, brethren, covet
to prophesy, and forbid not to speak with tongues. 1Co 14:40 Let all
things be done decently and in order.
This Pauline method is very similar to that (usually) practiced on this site! I also notice that no one talks over the other in Job.
Related:
How can we determine if a text is sarcastic?
What does it mean “to quench” in 1 Thessalonians 5:19? (see my answer)
However, I don't really think that is the answer (anymore). Please notice this snippet from the Jewish Encyclopedia which shows the deep reverence that was accorded to the chief rabbis:
The honor paid to the Rabbis exceeded even that due to parents. The "elder in knowledge" was revered even more than the "elder in years" (Ḳid. 32b). "When the nasi enters the assembly the people rise, standing till he bids them sit down; when the ab bet din enters, they form a row on each side of him, standing till he takes his seat; when a ḥakam enters, each one rises as the wise man passes him" (Hor. 13b; comp. Ḳid. 33b).
The rabbi or ḥakam lectured before the Talmud students at the bet ha-midrash or yeshibah. He seldom spoke in public except on the days of Kallah, i.e., during the months of Elul and Adar (Ber. 8b), and on the Sabbaths immediately preceding the holy days, when he informed the people of the laws and customs governing the approaching festivals. The rabbi who was a haggadist or maggid preached before a multitude of men, women, and children (Ḥag. 3a). A short sermon was delivered by him every Sabbath after the reading of the Pentateuchal portion (Soṭah 41a; Beẓah 38b). With regard to preaching on fast-days, funerals, and special occasions see Kallah; Maggid; Yeshibah.
It seems likely that the men of these divisions provided such a seat for their "rabbis". This seems to have devolved in Corinth into an exaltation of men in a mock honor, repeating what Jesus had rebuked in regard to the Pharisees:
[Mat 23:6 NASB] (6) "They love the place of honor at banquets and the chief seats in the synagogues
[Mar 12:39 NASB] (39) and chief seats in the synagogues and places of honor at banquets,
[Luk 11:43 NASB] (43) "Woe to you Pharisees! For you love the chief seats in the synagogues and the respectful greetings in the market places.
[Luk 20:46 NASB] (46) "Beware of the scribes, who like to walk around in long robes, and love respectful greetings in the market places, and chief seats in the synagogues and places of honor at banquets,