The Gemara emphasizes the great lengths one must go to in order to stay away from machlokes. The Gemara quotes the possuk in Mishlei (משלי יד) חכמת נשים בנתה ביתה ואולת בידיה תהרסנו the wise woman builds her home, and the foolish one ruins it with her own hands, in reference to אשת און בן פלת. The wife of און tried to reason with him using logic, in order to dissuade him from joining Korach's party. She told him that whatever the outcome of the argument, he has nothing to gain. Regardless of who wins, he will remain with the status of a talmid, and in any case will not be promoted to being a leader or Kohen Gadol of the generation. He accepted her argument, but told her that he had already pledged his loyalty with a שבועה, an oath, to Korach. She told him that she would resolve that problem.
Indeed, she gave her husband some wine to drink, and he went to sleep. She then advanced to the doorway of their tent and exposed her hair. She reasoned that surely Korach and his entourage would scrupulously guard the sanctity of their eyes and would not attempt to come close to her home if she was standing there with her hair exposed. She went to great lengths, risking her reputation as well as the holiness of her home, in order to ensure that her husband would not take part in a machlokes. She paid a great price; but no price is too large for the sake of avoiding machlokes. Thus, the Gemara says 'a wise woman builds her home'.
The latter part of the verse is a reference to Korach's wife. She persuaded him to start the machlokes, and urged him to see it through to its bitter end. Her husband was a distinguished personality who was supposed to have an important position in Klal Yisroel, ואולת בידיה תהרסנו and with her own hands she brought his eternal downfall upon him.
Whoever takes a part in a machlokes, however minute, will be considered liable for enabling the machlokes to continue. Conversely, one who attempts to settle a machlokes will be judged favorably for their attempts.
The Chida explains to which great lengths the wife of און בן פלת went in order to dissuade her husband from joining Korach's feuding team. The Gemara (יומא מז.) tells us about Kimches - a righteous woman who merited seven sons who served as Kohanim Gedolim. When the Chachomim asked her how she merited such a great privilege, she credited this to her extraordinary vigilance in covering her hair. She said that even the beams of her home never saw her hair uncovered. Oin's wife exposed her hair, and then reasoned with her husband that now that she desecrated the holiness of his home, neither he nor any of their sons would merit כהונה גדולה. Hence, he has nothing to gain from joining Korach in his fight for the כהונה גדולה! (חיד״א - כסא רחמים אבות דרבי נתן פרק לה)