Usually when a user complains about getting insulted by another user, a moderator reviews the claim, and when they feel that the complaint is warranted, they punish the insulting user as appropriate.
But how should I as a moderator act when I feel insulted by a user? As an involved party I obviously have a conflict of interest and am not objective. When I punish the user, there will be claims that I abuse my moderator rights to shut down people who don't agree with me. When I don't punish the user, people will think that it is OK to treat me that way and I will lose my authority.