Every disagreement which is for the sake of heaven will endure, and that which is not for the sake of heaven will not endure. -- Mishna The above line is very puzzling. The Mishna seems to be saying that if we disagree with someone genuinely and honestly, without ill intent (for heaven's sake), then that disagreement will continue. Why would we want a controversy to recur? Typically, we prefer that disagreements and arguments end. We assume that if both parties are well-intentioned, they will fix the dispute quickly and amicably.
As a society, we see ourselves as conflict-averse. Any disagreement is a bad thing and should be avoided. As such, we tend to see a prolonged conflict as a sign of bad faith. The Torah doesn't share this attitude. In Judaism, we see dispute and argument as core to the human condition. Different people will inevitably take different views on an issue, and this is not merely something to be tolerated but actively encouraged. We want people to think and question, not merely do what they are told or what seems socially felicitous.
In our Parsha, we see a clear example of a dishonest dispute. Korach comes to Moshe and Aharon and calls them greedy and power-hungry because they have taken the nation's two most senior leadership roles. Of course, Hashem immediately suggests a method for resolving this dispute. Korach can approach the Tent of Meeting bearing the incense offering, a priestly prerogative reserved for Aharon and his family. If Korach is worthy of such an honour, it will be accepted. If not, it will be rejected, with catastrophic results. Korach took advantage of this opportunity, apparently unphased by the risk.
The mark of an actual bad-faith dispute is the mark of Korach. It is demanding a resolution in your favour immediately. A disagreement for heaven's sake might not quickly resolve, and that's ok because both sides are coming with sound arguments for the right reasons. It might be that we feel some discomfort at that moment. The argument is not always pleasant. However, if we come with the right intentions, we can be satisfied that the dispute will end not with the rejection of one side. In our culture, we like to win arguments. Perhaps we should instead focus on hoping that neither side should lose.