To dream that you are breaking up with someone, indicates that there are feelings or situations in your life that you want to be rid of.

To dream that you did not break up with your ex, denotes that you are unwilling to let go of your memories and the past. Perhaps your mind may not have accepted the notion that the relationship is over.

To dream that someone is breaking up with you, means that you have low self-esteem. The dream could also be a straight-forward fear of rejection.