Although we are studying parashas Balak and not parashas Korach, it is still the correct time to discuss the severeness of machlokes, and how cautious we must be. As we mentioned, at the beginning of Korach, Rashi writes, נדרשת יפה זו פרשה "This parashah is beautifully taught..." The Pri Megadim (תיבת קהלת ה"ד גומא) writes, "People say (הלצה בלשון, in a light note) that it is always the correct time to discuss the evils of machlokes. It is נדרשת יפה, always the right time to speak about it, because "There isn't a moment when there isn't a machlokes. It is always the right topic to discuss."
An essential solution for machlokes is to remain silent. Silence resolves a lot of problems. As a wise person said, "When I am silent, I rule over my words, but when I speak, the words rule over me." No one knows what you are thinking. If you can keep your thoughts to yourself, this can avoid a lot of machlokes. But after you speak, a machlokes can ensue.
Reb Noson Gestetner zt'l said in the name of the Chazon Ish zy'a: Two things a person will never regret doing: (1) Learning Torah. (2) Remaining Silent.
The Gemara (Sanhedrin 105b) tells the discussion that Bilaam had with the donkey. When the officers of Moav (מואב שרי) saw the hardship the donkey was causing Bilaam, they asked Bilaam why he didn't choose to ride on a horse. He told them that he generally rides on a horse, but now his horse was eating in a pasture, so he had to take the donkey. The donkey immediately spoke up and said (22:30) ָאֲתֹנְך א ָנֹכִי הֲלוֹא, "I am your donkey." Implying, "You always take me on your trips. It isn't as you say that you generally take a horse."
Bilaam wanted to seem as someone who tells the truth, so he explained that he uses the donkey to carry the loads, but he rides on a horse. The donkey spoke up again, ֶׁראֲש עָלַי ָּרָכ ַבְת, you use me for riding. Bilaam said that it is only for rare situations. So, the donkey said ה ַזֶּה ה ַיּוֹם עַד מֵעוֹדְךָ, that he always uses the donkey to ride on for his trips.
The donkey then revealed more information that was very embarrassing for Bilaam. If Bilaam had remained silent at the beginning when the donkey said that he rode it, he would have saved himself a lot of shame and disgrace. But he felt that he must "have the last word", and this resulted in immense public shame. This tells us that when one is מדותיו על מעביר, and he doesn't answer back to those who embarrass them, in addition to the reward he will receive from heaven for this, he saves himself from a lot of shame and disgrace and heartache.
Someone came to Reb Naftali Amsterdam zt'l. He said that he doesn't have shalom bayis, but he wasn't able to divorce his wife. Therefore, he requested a רבנים מאה היתר. As they were speaking, this man said terrible lashon harah about his wife. Reb Naftali said, "How confused people are. They seek a heter from 100 rabbanim (not one less) to marry a second wife, which isn't a torah prohibition. But to speak lashon hara, they speak freely, and they don't seek a heter from not even one Rav!