In Pirkei Avot 5:17, there is a Mishna that says:
“Any Machloket that is for the sake of heaven will last, any Machloket that is not for the sake of heaven will not. What is a Machloket for the sake of heaven? Hillel and Shammai’s Machloket. What is a Machloket that is not for the sake of heaven? Korach and his followers’ Machloket.”
There is a strange inconsistency in this Mishna. Hillel and Shammai’s Machloket was between Hillel and Shammai but Korach and his followers Machloket was between Korach and Moshe, not Korach and his followers. Why is Moshe’s role not mentioned?
In addition, why would Hashem want a Machloket? Even if it is an argument strictly for the sake of finding the correct Halacha with no anger between the two parties, why would Hashem want to have a wrong opinion continue to exist?
There is a story in the Gemara in which Rabbi Eliezer and the Chachamim were in a Machloket. In order to prove his point he said, “If I am right, this carob tree will prove it” and the carob tree left the spot where it was planted. However, the Chachamim said “we do not take proofs from carob trees.” So Rabbi Eliezer said, “If I am right, this stream will prove it” and the stream suddenly began to flow uphill.
“We do not take proofs from streams” they replied.
Finally Rabbi Eliezer said, “If I am right heaven will prove it” and a voice from heaven came and said that he was right. Despite everything he had done the Chachamim still were not convinced.
“The Torah is not in heaven,” (Devarim 30:12) they said.
This story tells us something important about a Machloket on a Halacha. The Torah was given to us, and it is in our hands to derive the Halachot from it. As long as we reach an opinion based on the rules for analyzing the Torah, it is right. When there are conflicting opinions, we follow the majority.
The Machloket between Korach and Moshe was not a Machloket. Moshe derived his opinion by following the rules of the Torah while Korach did not. Therefore the only right opinion was Moshe’s and there was no argument.
So then why did the Mishna say “Korach and his followers’ Machloket”?
Korach wanted to claim the Kehuna without concern for who had it. Bnai Reuven wanted to claim their firstborn rights without concern for the Leviim, who already had them etc… Each person was doing it for his own personal interest, with no regard for anyone else. Every man was for himself- there’s no code among thieves. The Machloket of Korach and his followers actually was between Korach and his followers.