Vayikra/Leviticus 19:17
Lo-tisna et-achicha bilvavecha hoche’ach tochiach et-amitecha velo-tisa alav chet.
You shall not hate your brother in your heart. Rebuking, rebuke your associate, and not bear sin because of him.

It is forbidden to embarrass or shame another person. Even if we mean well, or we are trying to teach him a lesson and correct a wrong deed, we must be careful to say the right thing in a proper way and never cause another person embarrassment.

On one occasion, Rabbi Aaron of Belz was informed that one of the town’s residents had desecrated the Shabbat. He immediately ordered both the informer and the Shabbat violator to appear before him. "I order you to donate two pounds of candles to the synagogue," said Rabbi Aaron to the informer, "in order to atone for the fact that you spoke negatively of a fellow Jew." And you," said the Rebbe to the second man, "I fine one pound of candles, for being the cause of your fellow Jews speaking negatively of another Jew."

The informer sinned in regard to lashon hara (evil speaking) toward his fellow Jew.

Mishle/Proverbs 12:18
There is one who speaks rashly like the piercing of a sword, But the tongue of the wise heals.

Galatians 6:1
Brothers, even if a man is caught in some fault, you who are spiritual must restore such a one in a spirit of gentleness; looking to yourself so that you also aren’t tempted.

One doesn't necessarily have to be tempted in the same sin that the person corrected is caught in. But the temptation can come in how we correct the person.

Ya'akov/James 3:2

For we all stumble in many ways; if someone does not stumble in what he says, he is a mature man who can bridle his whole body.

This is why it is important to restore the sinner with gentleness.

This is also why we must first correct them in private.

Matthew 18:15
Moreover, if your brother commits a sin against you, go and show him his fault—but privately, just between the two of you.

Shalom v'brakhot v'simcha,
Moreh Chizkiyah Shlomo (Carl)