“Speak to Aaron and to his sons, saying: This is the law of the sin-offering: in the place where the burnt-offering is killed shall the sin-offering be killed before Hashem.”
The Gemora says that the reason the two offerings were brought and slaughtered in the same place was in order to save those who sinned from embarrassment. When people saw the animals being brought by a person they would not know if it was for a sin offering or a burnt offering.
From here we see that we should not cause others to become embarrassed when they have done something wrong. Similarly the Chofetz chaim in his sefer on the laws of Loshon Hora says that a person listening to Loshon Hora when in a group setting should be careful not to rebuke his fellow, rather he should wait until later when they are alone to rebuke Him as to not cause Him embarrassment over his sin!
