In political discussions I often find people using talking points; these are not in themselves invalid; sometimes it's nice to have a small library of concise, tightly-argued, emotionally-appropriate and tested frozen arguments that can be applied in a number of conversations. Provided they're being used in situations where they fit, they haven't already been shown to be flawed (based on false facts, fuzzy thinking, or shown to be inconsistent with the rest of one's values), and one has the ability to think outside of them, use of them is fine. I think we should avoid talking points that are empty; that only have the power to sway because they embrace or build on logical fallacy, or that don't have any substance at all; those that just express anger rather than norms, or that encourage people not to understand what they're talking about, they should be discarded.
Sometimes I get the feeling from people I'm talking with that I've pushed into territory of something that's a close cousin to talking points; planks in their internal emotional structuring on some issue. These usually are load-bearing for their perspective, but they're also not meant to be exposed in argument (not sure if I pushed the conversation in unexpected directions for them that I'm seeing these planks, or if they panicked and spat out the plank because on first glance it seemed to resemble a talking point). They only work because they fence off one's own doubt on a topic with a cheery slogan and a keep-out sign, and that lack of challenge or investigation protects the belief.
Load-bearing planks are usually delivered, in my experience, with the markers of panic; suddenly emotive language and strange body language if you ever see someone deliver them in person; when they're coherent enough to be logical fallacies, they're fallacies of the sort that aim to fence off the inquiry they're afraid of; false dichotomy is particularly common.
My normal response to these is to gently and sympathetically undermine the plank and then walk away. I've never had that killer instinct that I've seen in past friends who came to understand psychology of rhetoric in the way that I do; those friends typically used these situations to pounce and rip apart the worldview. I recognise that may be effective to neutralise an opponent, particularly if they'll otherwise head back to their community to pull things back together, but I think angling for that initially makes it hard to establish the trust needed to have a thoughtful dialogue, and it probably creates a power dyanmic that's unhealthy in the longer term (for both parties).
The fun thing about the way that people argue is that they use talking points (and these kinds of planks) without thinking. When people become aware of the structure of arguments and should they have the ability to do so, I think they're generally best off replacing those planks with more structured reasoning, perhaps through the process of seeking reflective equilibrium.
Most recently this came up in a discussion on politics that wandered into religion; I hold that the "either Jesus was a liar or a madman or messiah" is more of an internal plank than an actual talking point; it's too easy to pull apart to be voluntarily used externally, but through a gentleman's agreement with oneself it can save one from uncomfortable questions.