Any dispute that is for the sake of Heaven is destined to endure; one that is not for the sake of Heaven is not destined to endure. Which dispute is for the sake of Heaven? The dispute between Hillel and Shamai. Which dispute is not for the sake of Heaven? The dispute of Korach and all his company.
From our mishnah, it seems that dispute is positive, as Rabbeinu Yonah explains, “The intention is that the dispute will exist forever, today they will dispute over one thing and tomorrow over another thing…and furthermore, length of days and years of life they will add to them.” Rabbeinu Yonah is referring to a dispute “for the sake of Heaven.” On the other hand, a dispute that is not for the sake of Heaven will not endure, for when the first dispute arises, the two sides will separate and the connection between them will terminate. Furthermore, according to one of the versions,  our mishnah is connected to the previous mishnah, “a love that is not dependent on something never ceases.” According to this, it seems that a dispute for the sake of Heaven parallels love that never ceases. But how then, can this dispute exist forever? In a dispute, one of the parties is errant!
If the parties in a dispute are disputing “for the sake of Heaven,” their dispute is in order to reveal God’s Name – which is loftier than both sides of the dispute. Thus, both sides of the dispute for the sake of Heaven have a true basis. This is true, for example, regarding the existential dispute between the material and the spiritual: Just as God is not material, God forbid, so He is not ‘spiritual’ (for any definition like this is limiting). Thus, He is above the dispute, making it possible for both sides to maintain their positions.
This is true of any dispute for the sake of Heaven: “Both these and those are the words of the Living God.” For God, there can be many answers and they can all be truth. By voicing their different opinions, the parties to the dispute reveal the different ‘aspects’ of God, as it were, until “From this and from that God will be praised.” Thus, their dispute can endure, for the more they disagree, the more God is revealed and praised.
The problem begins when one side (at least) does not try to reflect God’s word as it is Above. From this position, the person disconnects himself from God. This type of dispute will not endure. The way of the world is that a dispute that is not for the sake of Heaven will destroy all the parties partaking in it. This is the reason that the example in our mishnah of a dispute that is not for the sake of Heaven is the dispute of “Korach and his company” and not “Korach and Moses.” Moses was not a part of the dispute at all. Instead, Korach created a certain image of Moses, which he disputed. As Rebbe Nachman of Breslev said of those who opposed him: “They do not have a dispute with me at all. They dispute the person whom they have conjured up in their imagination. And it is certainly worthy to oppose that type of person (the imaginary image that the opponents created for him).”
 Midrash Shmuel.
 Pirkei Avot 5:16.
 Eruvin 13b; Gittin 6b.
 Sotah 40a.
 Sichot HaRa”N 182.