If that were true, there would be no need to mediate. Of course people who disagree can mediate, just like people who are angry can mediate and people who don’t really like each other can mediate. All they have to do is agree to mediate, not agree upon every issue between them. Mediators do not expect their clients to talk quietly and never raise their voices, and a mediator truly has to feel comfortable being in the middle of people expressing anger and frustration, often times loudly. The mediator’s job, through restating and reframing what a party says and asking questions, is to get them to really hear what the other is saying and feeling and then see where they have shared interests to brainstorm resolutions where those interests can be met for both of them.