Just about every atheist has encountered and dealt with an apologist at some point (and usually multiple times, too). How often, though, have you had to deal with a truly honest apologist? By "honest," I mean someone who rejects bad arguments, sticks with good arguments, and regards the failure of an argument as an indictment of their position.
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Frankly, I don't think I've ever dealt with a truly honest apologist. In my experience, apologists latch on to arguments that they think look good and will continue using them over and over no matter what sorts of responses they hear from others. Counter-arguments mean nothing and even if they concede an argument's failure, they will turn around and use it again later with others.
I have gotten similar reports from other atheists about their encounters with apologists. For apologists, the only goal is spreading their ideology, not a quest for better understanding of the truth. Reasoning and arguments are tools of persuasion regardless of the truth and regardless of the qualities of those tools.
To a skeptic, if an argument is good enough to use to support a proposition, then its failure contradicts the proposition, or at least calls the truth of that proposition into serious question. If I believe something because of an argument, then if the argument fails the belief should fail too. If I believe something not because of some particular argument, then it seems dishonest to use that argument to support the belief.
For example, I believe that communism is better than capitalism because I believe the social ownership of the means of production would lead to more happiness and satisfaction in the world. I justify my communism on purely pragmatic grounds. If someone shows me that communism, or some aspect thereof, would lead to a worse outcome, then I will change my conception.
For example, we know from experience that while it might be effective at quickly industrializing a poorly-industrialized country, unconstrained political rule by a self-selecting party elite has serious negative consequences when industrialization reaches a certain stage. I therefore abandon the idea of such a party elite. If the theory does not fit the facts, the theory must change.
An apologist, on the other hand, in some sense "just believes." The arguments and reasons proffered really have nothing to do with the foundation of the apologist's beliefs; the arguments are tools only of persuasion, not justification. Either the belief is mystical, revelatory, or the actual foundations of belief are at best subconscious and at worst intentionally covert.
Hence, to a certain extent, arguing with apologists is an exercise in futility. A rebuttal has no effect; they do no believe because of the argument, so even a decisive rebuttal does not undermine the belief. Furthermore, even showing that the argumentation is disingenuous in this sense is such a subtle point that only someone with considerable education, training, and experience in critical thinking and rational belief formation can spot the disingenuity, and those people are already strongly predisposed against mystical or covert belief.
Source: The Barefoot Bum
So why even bother arguing with apologists? The author here says that it can provide insight into what sort of questions need to be asked. I'm not sure that even that is enough, though, give how much time can be wasted with an apologist.
This is especially true when you consider the fact that few apologists ever offer anything new. In the context of Christianity, for example, there's a standard set of stock arguments which every apologist tries to use. Sometimes not even the formulation and words change very much.
You can't really learn much from people who themselves are uninterested in learning anything new themselves.