I think the secret is not to "argue," but, rather, to "respectfully disagree." Some of the more arrogant hosts are looking for a good fight so they can yell and eventually hang up. When they do this to a respectful caller who is making sense, the host ends up looking like a bully. A good host, no matter how theatrical his or her shtick, wants to sound intelligent and win an argument on points. And they welcome callers with opposing viewpoints, because disagreement is what makes the show exciting. The problem for the hosts is how to end a call when they realize that their argument is neither discrediting the caller's position nor persuading the caller to change his or her mind. No host wants to say, "Mmmm, you know, you're right," although I have heard hosts concede technical points to experts. Even Rush occasionally admits to being wrong, but then congratulates the caller for being part of that small elite able to challenge his "98% of the time" record.
But the caller has to guage the mood and rhythm of the show and the style of its host. A high energy host, whether liberal or conservative, doesn't want his stride broken by a boring, cerebral discussion, no matter how substantive, and a measured Barry Farber-type host doesn't want callers who rant and rave or are too shallow to engage in a legitimate dialog. As a liberal, my tactic would be to show the host that I am not a mindless left wing Kool-Aid drinker, that my thoughts are my own, and that I am willing and able to defend my positions, not only with facts, but with logic. And, even if the host beat a hasty retreat to take another call, my hope would be that others would call to say that I had a point, even if they didn't fully agree with me.
Phil Boyce says that a host should not lose control of the show to the callers. But, then, it is the callers that make the show accessible to the listeners, so it is a symbiotic relationship. The listeners react to the host, and then to the callers, and then, when something strikes a responsive chord, or fails to, the listener feels like calling (although most never do). So, unlike television and non-call radio shows, which are purely spectatorial, talk radio involves the listener. Hosts who undermine that involvement by insulting or intimidating callers, and thus, the listeners, do themselves and their audience a disservice, and the high ratings this kind of pap brings in lowers the bar for everyone. But, hey, that's showbiz.