In person, I have no time to think about what the other person is saying and respond based on that consideration. I can prepare what I'm going to say, but if the other person has a perspective that I hadn't considered, then I don't have time for careful consideration. I can try to "win" by overcoming his perspective with the strength of my ideas, but that solution removes the possibility that we'll find a better answer that incorporates both of our perspectives. I can try to listen and consider his perspective during the conversation, but in doing so, I risk letting him "win" by overcoming my position while I think about what he's said.
The beauty of some form of written discussion is that I can carefully consider every point in context. I can let whatever emotion arises within me play itself out before trying to respond. I don't have to spend energy fighting the emotion. I can let the emotion blow through my mind like a storm and then consider things when I find the calm on the other side. I can read the other person's words over and over in order to understand whether his positions are internally consistent. If the discussion leads us to a better idea, I can find that idea more easily. If the discussion only proves me right, then I can explain more carefully exactly why I'm right.
Of course, the other side of this coin is that much of communication is not only in the words. In writing, we lose body language and voice tone completely. If both people in the discussion have some skill in writing what they want to say, then this loss can be overcome. If one or both of them cannot communicate well using only the words, then the loss is nearly impossible to overcome.