In order to correct someone without making them feel embarrassed or angry, you must take special care when doing so. Firstly, always make sure that you address the person directly and do not try to correct them in front of a group of people. This will only embarrass them and make the situation even worse.
Alternate approaches to addressing a comment
If you feel that someone has made an offensive comment, there are several alternative approaches to addressing the issue without embarrassing or angering them. The best approach is to ask questions to clarify the situation. This is more effective than making assumptions about the person's political views or intent. Moreover, assuming that someone is intentionally offensive can only put them on the defensive and is unlikely to change their behavior in the long run.
Using questions when correcting someone
When correcting someone, using questions can make your correction feel less aggressive and more friendly. Instead of simply reiterating what you believe is wrong, pose a question and ask for further details. Then, you can explain your point of view in an empathetic way.
It may not be easy to correct someone in front of others, but if you use questions and make the person think you are asking for clarification, you can soften the correction. Try to use humor, as it can help you soften your tone of voice. However, if you don't know any jokes, you should still correct the person in a gentle manner. Remember that the tone of voice conveys just as much as the words you use.
Avoiding sounding like a domineering know-it-all
When correcting someone, it's very important to avoid sounding like a know-it-all. A know-it-all's behavior is often a coping mechanism to cope with underlying issues in their life. Moreover, knowing-it-alls are often unaware of the effect that their behavior has on others. Consequently, teachers should be very careful about calling these people out.
The first thing to remember is that know-it-alls hate being proved wrong. It ruins their world view. Instead of admitting that they are wrong, they label others as ignorant or stupid.