Let me try a Hansonian explanation: conversation is not about exchanging information. It is about defining and reinforcing social bonds and status hierarchies. You don't chit-chat about the weather because you really want to consider how recent local atmospheric patterns relate to long-run trends, you do it to show that you care about the other person. If you actually cared about the weather, you would excuse yourself and consult the nearest meteorologist.

Written communication probably escapes this mechanism - the mental machinery for social interaction is less involved, and the mental machinery for analytical judgment has more room to operate. This probably happens because there was no written word in the evolutionary context, so we didn't evolve to apply our social interaction machinery to it. A second reason is that written communication is relatively easily divorced from the writer - you can encounter a written argument over vast spatial or temporal separation - so the cues that kick the social brain into gear are absent or subdued. The result, as you point out, it is easier to critically engage with a written argument than a spoken one.