We have an obligation to be extremely careful not to do or say anything that will constitute even a minor slight to the honor and respect due another person. However, if someone insults us, we should tolerate what they say and still strive to be kind to that person.
Of course, this is not an easy level to reach. It takes much hard work and effort to train yourself to ignore the insults of others. If a person identifies himself as a body, it is truly difficult to develop these antithetical positions.
By realizing that you are a soul, however, you will be aware of having been created in the image of the Almighty. Why is this important? Because tolerating insults is part of the commandment to emulate the Almighty - Who bestows life upon us even when we do things that are against His will!
Today, if someone insults you, focus on the following thought: Other people's insults do not really cause you harm.
(see Tomar Dvorah; Rabbi Yechezkail Levenstein - Ohr Yechezkail, Midos, pp. 90-1; Rabbi Pliskin's "Consulting the Wise")