The Key to Negotiating: Focus on the What, not the Why
In a contentious negotiation between separating business partners (or marriage partners), the participants tend to focus on the why rather than the what, which is the opposite of what they should be doing.
When you focus on the why in a negotiation, you're trying to convince the other party of the righteousness of your position and demands; how you're the injured party; that the other side is going to have to pay to undo the damage. In focusing on the why, you also convince yourself of the intractability of your own position--you sell yourself, you dig your heels in. Negotiations based on why are fights to the death, the nuclear option, the Coliseum. Think Game of Thrones.
If you focus on the what, on the other hand, you think about the things you need and the things you want in a deal (and you know the distinction between needs and wants). You consider objectively. You can make a list: here's what I need to get this deal done.
If you have a volatile negotiating partner, a mediator can be a useful third party in a negotiation based on what. Let each side state their needs in a preliminary meeting, then separate into different rooms. The mediator discusses the other side's whats with one participant and together they decide the items they can live with and which they cannot. They discuss their own whats and which ones they are willing to trade if the other party will back off on one or more of their own whats. Back and forth it goes until what is sifted out is an agreement in which both sides get most of what they need and some of what they want. They may even shake hands at the end.