As we said in the previous mitzvah, it is a responsibility on every Jew to correct the behavior of others wherever possible. But it is only a mitzvah to do so in the proper way! Shaming someone publicly is actually a sin!
The Sefer HaChinuch cites the Sifra on this verse that we should repeatedly rebuke someone, even several times. It then asks, “But what about if the person’s face changes from embarrassment?” No, the Midrash answers, then we do not rebuke him because the verse concludes with “and not bear a sin because of him.”
The Talmud (Baba Metzia 59a) tells us that it would be better for a person to allow himself to be tossed into a furnace than to willingly embarrass another person. (This is derived from Tamar, who was willing to be burned rather than shame Yehuda in Genesis chapter 38.) On the previous page (58b), the Talmud says that one who shames another in public, causing the blood to drain from his face, is comparable to a murderer.
The reason for this mitzvah is obvious: nobody likes to be embarrassed. In the context of rebuke, it can also make a huge impact on the outcome. If properly corrected, a person might change his ways. This is good for the person and it’s good for society. But if someone is called out in public, he’ll be embarrassed, angry, and resentful. He’ll hate the one who rebuked him and probably become more stubborn in his ways out of spite. It’s a bad scene. But even outside the context of rebuke, we must be careful not to shame others.
This mitzvah applies to both men and women in all times and places. In the Talmud, it is discussed in tractate Shabbos on pages 54b-55a, in Arachin on page 16b, and elsewhere. It is codified in the Mishneh Torah in the third chapter of Hilchos Choveil u’Mazik. This prohibition is #303 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #79 of the 194 negative mitzvos that can be fulfilled today as listed in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim.