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Sites like Twitter have catalyzed a transformation in the way people argue over politics, by making popular the use of talking points: short objections that serve as "gotchas" to particular points of view, and which can be used roughly independently of the specific manner in which the point of view is presented. Here, I'll analyze the origin and function of talking points.
Thoughts have an explicit content, and, underlying that, an implicit content which is brought out through discussion.
To discuss the problem with these in more detail, we need to discuss the process by which thoughts are generally formed. In the original formation of every thought there is a series of cognitions, judgements, relations, and so on that lead to the thought, and which are contained implicitly in the thought. They are, however, not explicit in the thought.
This is why, for instance, debugging code or proofreading an essay gets harder the further away you do it from the point of original creation: one day after you originally wrote the code or essay, you know the intent of any given line or paragraph, why you chose to word it in the way you did, and so on; perhaps you still remember the alternatives you tried and rejected. This is all implicitly contained in the creation of the product, but not explicitly contained in it. But one month after writing, most of the implicit content has faded away, leaving only the explicit content that you see on the screen; it is much harder to improve on the explicit content without the implicit content. (This is strongly related to the notion of tacit knowledge).
Engaging with the bearer of the thought, concerning the thought, involves much the same as improving code or an essay with the person who has written it: to draw out, generally via a dialectical$^1$ process, individual components of the implicit content of the thought, and to critique or revise these one at a time. According to the logical form of the thought, the entire will slowly be revised insofar as its implicit parts require demand this due to inconsistency.
For instance, if the thought relies fundamentally on induction, "X tends to be like Y", engagement with the goal of dissuading them from this thought would generally look like this: to elicit from the bearer of the thought what they view to be a few central examples of X that, in their view, tend to be Y,
Elicit from the bearer of the thought what they view to be a few central examples of X that, in their view, tend to be Y.
Determine why they believe these examples to be central; reason about whether they are specific cases, formed perhaps by biases in the bearer's observation.
For instance, if someone believes that Vietnamese food is terrible, you might ask what Vietnamese food they had tried that led them to this conclusion; if they respond that their experience of it is with Vietnamese restaurants in Missouri, you might respond that Vietnamese restaurants in Missouri are in no way an exemplar of Vietnamese food in general, perhaps offering some better examples. If they are amenable to this, the logical form of induction would demand that they revise their thought, and they would hopefully drop the belief that Vietnamese food is terrible.
Note, however, that it was the implicit content of this thought that caused them to form it (their experience with Vietnamese restaurants), and which must be critiqued in order to change the explicit content.
Alternatively, determine why they've inferred Y in particular from X; perhaps this was the wrong conclusion to make. A bombastic example to illustrate the general point: if someone thinks that pistachios are terrible, having tried examples from many different places, you may ask them how they eat it, only to find out that they don't unshell pistachios before eating them. It would be improper to reason that something is terrible after using it if you don't use it in the manner it is intended to be used, so in particular it's improper to reason that pistachios are terrible for eating if you do not eat them without first removing their shells.
Such discussions necessitate that the bearer of the thought being discussed have access not only to the explicit form of the thought, but to the implicit form: the entire tree of cognitions, judgements, and observations leading to and supporting the explicit form.
Why social media incentivizes the stripping from thoughts of their implicit content, a.k.a. their decapitation.
Should this implicit form be lacking, attempts to engage with this thought will be far less productive: either an implicit form will have to be built ad hoc, or the thought will have to be countered flat out (this is only possible when it is explicitly and inarguably falsifiable via something directly observable, which is very rare).
Often, this ad hoc construction will be based on hearsay, incorrect repetition of things one's previously heard, and other logical constructions which, because they are being formed quickly and without reflection, are deeply flawed (attacks on them are often rebutted by more of the same, leading to a fractal wrongness).
In general, engagements with thoughts stripped of their implicit content, or decapitated thoughts, quickly lapse into incoherence, for the reasons above. This is not always true, especially not when the interlocutors are quick-witted and intelligent enough to build good ad hoc constructions, and are acting in good enough faith, but is in my opinion usually true.
How, then, does modern social media proliferate the content of these decapitated thoughts?
If we were to somehow measure the "size" of a thought — ignoring the fact that thoughts can rarely be cleanly separated from contexts and networks in which they live — we would find that the implicit form of the thought takes up the vast majority of the size, despite being the hardest to articulate (furthermore, it's very difficult to articulate outside of a dialectical context, which is why we often resort to ways of simulating dialectical contexts, such as rubber duck debugging). Hence, in mediums that incentivize short-form thought, such as social media sites meant for casual posting and browsing and whose reputation systems discourage posting things that will likely be skipped over, the easiest mode of communicating thoughts will simply be to decapitate them, stripping them of the extremely large and hard to articulate implicit content in favor of the short and simple explicit content.