When Korach challenged Moshe, Dasan and Aviram joined the fray. Although Moshe was certainly not at fault, nevertheless, he sought to appease them. To this end, Moshe sent a messenger to Dasan and Avirom requesting that they appear before him. Rashi cites the Medrash which deduces from Moshe's conduct that, "One should not maintain an argument, for we see that Moshe sent for them to make peace."
Rav Wolbe (Shiurei Chumash) notes that it is clear from Rashi that "not maintaining an argument" does not simply mean that one shouldn't fight. It means that one should make positive attempts to achieve peace. Moshe could have ignored Dasan and Avirom. Instead he attempted to initiate a meeting in order to placate them.
Although we should emulate Moshe's conduct, the ability to disagree without taking the argument personally is definitely not an easy trait to master. All too often, when people disagree, their difference of opinion snowballs into a full-fledged "war" which ultimately results in a situation where the two sides refuse to even speak to each other. What happened is, they took their difference of opinion personally and it affected their relationship.
A glimpse of a Torah true disagreement can be gleaned from the dispute between the pre-war European Yeshivos regarding the learning of Mussar. While Rav Baruch Ber Lebowitz zt"l was of the opinion that fulltime Torah study obviated the need for a set time for mussar study, the Alter of Slabodaka felt that today most boys need to compliment their Torah study with a daily regimen of Mussar. Thus, the Alter left Rav Baruch Ber's Yeshiva, Kenesses Beis YItzchok, and opened his own Yeshiva Kenesses Beis Yisrael. Sometime thereafter, Rav Baruch Ber took one of the Alter's most dedicated disciples as a son-in-law! Their dispute did not affect their relationship.
It is well known that Rav Shlomo Zalman Auerbach stated at his wife's funeral that they lived in peace together and thus there was no need for him to ask her forgiveness. Sometime later, he met a disciple who had recently got married. He asked how things were going, and the disciple responded that things are great and they never argue. Rav Shlomo Zalman then inquired if everything was alright with his wife and if she was healthy. The disciple responded that Baruch Hashem everything is fine, and inquired why Rav Shlomo Zalman was asking. Rav Shlomo Zalman said that it is not normal to have such a relationship without having any disagreements. "But didn't you yourself say that you did not have to ask your wife for forgiveness?" asked the bewildered disciple. "Absolutely," he responded. "Since our disagreements did not affect our relationship, there was no reason to ask for forgiveness!"
Life is full of disagreements but it is up to us to determine whether or not it will be full of fights!