If a first person knows that a second person does not accept a particular text as a valid reference, why would the first person continue to quote that text? In principle, this could occur with any subject. In practice I only see it with christians quoting the bible. Now, I have come up with some possibilities.
Too stupid to think of anything else to say. It is possible that someone might continue using the same failed tactic because he can't think of anything else. Such a person is not a useful advocate for any position.
Can't really say what he'd like. This condition suggests an indirect warning. He is repeating what is already considered invalid to ensure a rejection. He is forced to create the illusion of advocating an abhorrent position.
Puppet on a string. The first person isn't acting of his own power at all. Of course the same question can then be applied to the puppet-master.
Seeking an emotional response. Such a person is being dishonest in any debate. In internet forums, he is considered a troll.
Playing to a different audience. This would often be mixed with number 4. He is not really trying to convince the person to whom he is nominally speaking. Instead, he is putting on a show for people who agree with him.
So, can anyone think of any other possibilities? Or have I got them all?