Focus on the problem not the person is a phrase well known by people in the dispute resolution field. What does that mean for use in daily practical terms? How often have you found that the person you are in conflict with becomes the target of your ire instead of the actual problem or issue causing the conflict? When asked for a description of the problem the response is typically a character description of the person - he/she is being power hungry, control freak, unreasonable, sarcastic, unreliable, single-minded, and so forth. You encourage the person to pinpoint the offending behavior or action of the person, but they are unable or unwilling to look past the personality of the offender.
The danger in this scenario is in allowing the situation to become an intractable conflict, where both parties absolutely refuse to consider that the actual conflict can be resolved. Contributing to this phenomenon is an escalating need to be right. The parties fall into a trap that being right is more important than the relationship.
To avoid this trap, re-orient your thinking about the situation. Stay focused on the problem(s) causing the conflict. Begin by identifying the issue in conflict. Utilize joint problem-solving by inviting the other person to work with you in identifying multiple options for resolution. Work to identify your interests as well as theirs. The goal is to come to a mutually satisfactory solution/agreement, not on being right.