Many people are just not comfortable with face-to-face negotiations. Even when parties to a mediation are willing to meet for a joint session to discuss the circumstances of the conflict, they generally prefer to break into separate rooms when it comes time to negotiate a settlement. Sometimes I wonder why people don't behave in the opposite way. You might think they would be reluctant to reveal their trial evidence, or talk about personal issues in front of the opposing party and counsel. Instead they are more likely to wish to get these aspects of the dispute out in the open, while preferring secrecy when they are ready to make a deal. Perhaps that is because people doubt their skills as negotiators, and are afraid they will be out-negotiated, as in the amusing example below. Or perhaps they just need time to discuss their strategy privately with the mediator, who might be able to provide insight as to the other side's receptivity to their proposals.
For the most part, however, I think parties to a mediation prefer not to communicate offers and counter-offers face-to-face because they do not want to expose themselves directly to the other side. Making an offer can be seen as an act of bravado (if it is an aggressive offer), or it could taken as a display of weakness or vulnerability (if it is a conciliatory offer). Like asking someone for a date, making any kind of offer invites rejection, and people hate rejection. In addition, making an offer reveals the offeror's thought processes to the other side, in the same way that a poker player placing a bet on the table tells the other side something about the strength of his hand. Even if the poker player is hiding behind his best poker face and his darkest sunglasses, the amount he puts on the table is still a revealing gesture.
Perhaps this desire not to show one's hand explains the advent of online negotiating tools such as Cybersettle, which allows offers and counter-offers to be communicated online, without either side knowing the amount of those offers. Cybersettle only informs the parties of their numbers if they are within a set range of each other, thus allowing parties to close a deal only when they both know that a deal is within reach. It seems like a useful tool for parties who have already decided they want to settle, and just want to make sure that they do not offer more or less than they need to to close. The most important part of mediation, on the other hand, is the part that prepares the parties to enter the deal-making phase. Only after the parties have identified their interests and the business or personal issues that may be driving the dispute, and after they have fully considered the costs and risks of resolving the dispute in the courts, are parties ready to consider resolving a dispute by negotiated agreement. At that point, if the parties have reached the state of enlightenment that we all hope for, it should be relatively easy to make a deal, whether face-to-face or from separate rooms. But often, there is still a lot of negotiating work to do, and I don't begrudge the parties a little separation from the opposing party if that is what they prefer.