The dream of insulting someone represents repressed resentment towards that person, fear of rejection and disappointment, lack of self-confidence or self-worth, or a change in your relationship with that person.

Dreaming insulting someone symbolizes repressed anger towards that individual. This might be a family member, friend, a colleague. In this context, the dream is a way for your subconscious to release these toxic feelings of anger and frustration, that you might otherwise be unable to express in real life.
Related: Dreaming of quarreling with someone: Arguing in a dream
Your dream could also symbolize your lack of self-confidence and self-worth. If you find yourself insulting someone in a dream, it may be a reflection of how you feel about yourself in real life. It shows that you feel insecure or uncomfortable in certain situations.
The dream might indicate a change in your relationship with this person. It is possible the relationship is evolving in some way; hence, this dream is a way for your subconscious to process these changes.
A dream of insulting someone can reflect the fear of rejection or disappointment. This might be someone you have feelings for, such as a romantic interest, or it may be a boss or colleague you are hoping to impress. In such a case, the dream is a way for your subconscious mind to express your fear of being rejected or disappointed by this person in any way.