Our experience has been that mediations can break down when one or both parties approach the mediation session with the goal of proving that he/she is right as opposed to the goal of reaching a settlement and making the litigation go away.
Many times, a party to a dispute wants to be heard. In a courtroom setting, the lawyers do most of the talking and in a face to face meeting the other party, frustration and anger can boil over.
In a mediation, each party will have time to meet and speak with the mediator separately. You can make your point loudly and passionately without hesitation. A good mediator will reframe your position into a position that can move the two sides to an agreement. Hostile, direct confrontation will be avoided as this type of interaction rarely facilitates an agreement.