There are eight common reasons:
Caution your client that the road to client-directed negotiations is not without bumps, detours, and even washouts. I would estimate that only about one-half of my clients successfully negotiate all the items in the divorce agreement with minimal intervention from me. Negotiations are as unique and complex as the people involved.
For those of your clients who, for many of the eight reasons discussed above, cannot handle client-directed negotiations, experienced family law practitioners with good negotiating skills are a must. It is quite instructive to observe two master divorce attorneys negotiating. They are able to settle their cases very quickly beause they have no need to waste time extaneous matters, such as probing the weaknesses and strengths of the other side. They know each other, and they are familiar with the facts of their cases and the likely legal outcome. After an initial period of "testing" the other, each promptly realizes that she or he is dealing with a master negotiator, and a solution is often quickly worked out.
In fact, the only impediment to immediate settlement may be the lack of emotional readiness of their clients to proceed to closure. The experienced attorneys may have to wait for the parties to resolve their psychological separation and grieving processes before final papers can be signed. Truly professional expert matrimonial lawyers are not really negotiating. They are actually engaging in the art of compromise and accommodation. Each values the importance of establishing a common ground of interest, and knows better than to engage in the game of "winner take all". They need only communicate to the other side, as early as possible, their maximum concessions and the minimum concessions they expect in return. Through experience and training, they will reach a satisfactory settlement, usually through a process perhaps they are not even consciously aware of, such as subtle revelations or their weaknesses, tip-offs, or even subliminal messages.
Finally, there is an old lawyer cliche that a good settlement is one that completely satisfies neither party, but that each can live with. If your side wins too much and the opposition gets too little, the whole agreement is more apt to come unhinged and costly litigation may result. Where both sides feel that the terms are fair and reasonable and were reached by give and take, there are psychological and moral pressures to abide by the agreement, much in the same way you are honor-bound when you "shake on it".
Whether the client is able to engage in direct negotiations or must engage your services fully, I strongly recommend the client take a temperament test such as one set out in the Appendix hereto. The insights gained by both the client and the attorney are well worth the few minutes it takes to answer the questionnaire.