On the pasuk (45:15) עֲלֵהֶם וַיֵּבְךְּ אֶח ָיו לְכָל ֵּׁקוַיְנַש, "[Yosef] kissed all his brothers and wept over them"... The Shlah Hakadosh writes, "See how much a person should forgive others. They sinned against Yosef, and yet, Yosef cried and kissed them." They should be asking forgiveness from Yosef, but Yosef turned the situation around, and he appeased them.
The Midrash (Tanchuma 5) states, "Yosef placed himself in great danger. If they were to kill him, no one would save him. Why did Yosef say (45:1) מֵעָלָי אִישׁ כָל הוֹצִיאוּ, "Take everyone away from me"? Yosef thought to himself, "Better I be killed than to embarrass my brothers before the Egyptians." The Midrash elaborates on the great danger Yosef was in at this time. Even once they knew that he was Yosef, they wanted to kill him, until a malach came and dispersed the brothers to the four corners of the room. But Yosef was prepared for this. He preferred to die rather than to cause embarrassment to his brothers.
The Midrash (Psikta) writes that Yosef was cautious never to be alone with his father, so his father wouldn’t ask him where he was all these years, and he would end up telling him that his brothers sold him. (See also the Ramban, 45:27, that לו להגיד רצה לא הטוב במוסרו יוסף, Yosef, with his good middos and ways, didn't want to tell his father.)
Shem MiShmuel (5679) writes, "This is a great lesson for every person, to be cautious not to speak badly of others. It would certainly be a great thing if Yaakov and Yosef could be together. Certainly, great secrets of the Torah and tikunim, rectification of the worlds, would come from it. Nevertheless, Yosef didn't consider this great loss. It wasn't worth it for him, if that would mean he had to speak badly about his brothers."
The Gemara (Sanhedrin 11a) states that once, when Rabbeinu HaKadosh was giving a shiur, he smelled the scent of garlic and he said, "Whoever ate garlic should leave." Reb Chiya left, and then everyone left. The next morning, Reb Shimon, the son of Rebbe, said to Reb Chiya, "You caused my father distress." Rashi explains that he said this because he thought Reb Chiya had eaten the garlic. Reb Chiya replied, כזאת תהא לא ,ושלום חס בישראל. Rashi explains that he said that he didn't eat garlic; instead, he knew that the person who ate garlic would be embarrassed. So, Reb Chiya left, knowing that everyone would do the same, and this saved someone from shame.
The Maharsha explains the Gemara differently. He says that Reb Shimon, the son of Rebbe, understood that Reb Chiya didn't eat the garlic, but he felt that he should have stayed in the beis medresh and not left. Reb Shimon understood the reason Reb Chiya left the beis medresh, to save this person from shame. But he felt that it was still wrong. It caused so much bitul Torah! Wouldn't it be better that the culprit leave, even be ashamed, but for Torah study to continue?
Reb Chiya replied, "Chas v'shalom. This can't happen in Yisrael. Bitul Torah was worthwhile, if through it, a Yid was protected from shame."
It states (44:28) טֹרָף ט ָרֹף אַ ךְ וָאֹמַר מֵאִתִּי הָאֶחָד וַיֵּצֵא. The Chasam Sofer explains that ט ָרֹף means parnassah (see Tehillim 111:5, נתן טרף). It is known that one machlokes pushes away one hundred parnasahs (Shlah on Yoma, Derech Chaim, letter 44). The pasuk is hinting, מֵאִתִּי הָאֶחָד וַיֵּצֵא, if there will be machlokes, and there won't be unity, טֹרָף ט ָרֹף אַ ךְ וָאֹמַר, the parnassah will be ripped up and lost.
Special caution must be taken not to fight over which path in avodas Hashem is better. Rebbe Yechezkel of Kozmir zt'l said that this is hinted in Yosef's words (45:24) בַּדָּרֶ ךְ ת ִּ רְ גְּזוּ אַל, they shouldn’t argue about בַּדָּרֶ ךְ, the correct derech, path, in avodas Hashem. (written in Divrei Yisrael)
Beis Yaakov (Alexander, a student of Rebbe Bunim of Peshischa zt'l, p.203) writes, "I heard from my Rebbe that if a person has בנים גידול צער, hardships raising his children, r'l, the segulah is to be cautious from machlokes. He should run after peace, and be with the people who are humiliated and don’t answer back. This will be his cure."