This is a common phenomenon in most languages. It is an 'elliptical' phrase, which is derived from 'ellipsis', not 'squashed circle shape'. It means that part of the phraseology is left unspoken (elided), but the semantic content is 'understood' by the hearer/reader because they are familiar with the usage within that context.
The actual comparison in this instance of the phenomenon should be, "if you agree you 'nod [your head]'; if you disagree, you 'shake your head'. This correctly puts the emphasis on the use of 'nod' and removes it from 'shake'. And that eliminates most of the discussion of cultural and colloquial meanings and focuses attention on language structure, not usage.
If you become sensitive to this phenomenon, you will begin to notice its very ubiquitous influence. Almost every conversation you have will include, and most understandings will often hinge on, differing interpretations of statements in which elliptical phrases are central to the semantics.
It is also the foundation of most advertising slogans and almost all jokes. Which means it also has both visual and conceptual parallels. The basic proposition is that the context of our communication (meaning the conceptual grasp we have of our physical and intellectual environment) is subject to change based on the definitions that participants in a communication impose on the other participants. And it is proof that often the power and influence of a statement is based not on what is said, but what is not said. So a powerful or inspiring statement could build up a motivating context which the hearers might tend to identify with and then some aspect of the context can be left 'open' (the future, the contingencies, the key contribution, the missing link) and each listener then completes their internal context by filling in their personal impression of that unspoken item.
Salvador Dali's 'surrealism' is the most 'graphic' graphic example of the principle: introducing contrasting items will change our perception by altering the context of our internal, mental environment. The image is simply lines, spaces, and paint, but the semantics that Dali introduces forces the viewer to examine the process of how they internally assemble a semantic context of their moment-by-moment experience.
In the same way, a joke sets up a context that seems to mean one thing, but the punchline reveals that the context can and should be interpreted as something else entirely.
So the elliptical phrase is a key part of influencing people since it one of those flexible and malleable (can bend, can BE bent) components in the language capability that underlies all languages and constitutes the underlying logic that humans were given at their creation.