Wikipedia
Antiprocess is the preemptive recognition and marginalization of undesired information by the interplay of mental defense mechanisms: the subconscious compromises information that would cause cognitive dissonance. It is often used to describe a difficulty encountered when people with sharply contrasting viewpoints are attempting (and failing) to discuss a topic.
In other words, when one is debating with another, there may be a baffling disconnect despite one's apparent understanding of the argument. Despite the apparently sufficient understanding to formulate counter-arguments, the mind of the debater does not allow him to be swayed by that knowledge.
There are many instances on the Internet where antiprocess can be observed, but the prime location to see it is in Usenet discussion groups, where discussions tend to be highly polarized. In such debates, both sides appear to have a highly sophisticated understanding of the other position, yet neither side is swayed. As a result, the debate can continue for years without any progress being made.