Separating the people from the problem helps us to achieve win-win solutions by reducing the degree to which emotions become involved in the negotiation.
When negotiators focus on the people rather than the problems they tend to redefine their negotiations. They take something that could be integrative and make it into a distributive, zero-sum negotiation. They feel that making any concessions is an indication that they have lost in the personal competition between them and the opposing negotiator.
If negotiators can focus on the problem instead, they can see solutions that will benefit both sides. They will not be caught up in defeating the rival negotiator as a sign of their own superiority. This will allow for a win-win solution.