Question: There would be more double-negatives like these, but I specifically want to mention "This couldn't be further/farther from the truth".

When this phrase is used, it apparently incites the sense that "This couldn't be a lie, but much nearer to the truth". It isn't apparently recognizable as double-negative when someone(even with much familiarity with English speaking/listening) hears this for the first time, but innocently could interpret just the opposite that is mentioned above in quotes.

If the speaker had just used an additional term anymore/any/more in this then it could have made sense and become recognizable as double-negative "This couldn't be anymore further/father than truth". And to support this belief, let's compare this with "I couldn't care less", now when someone hears this phrase, it almost becomes clear that speaker shows "uncaring" attitude towards something/someone.

What could be the reason that these kinda "dubious" double-negatives came to be and widely used despite their inherent nature of inspiring "reverse" than what is intended meaning by the speaker ?

Answer: 
The phrase, couldn’t be farther from the truth, isn’t a double negative. It does mean what it says - that something is not true, and is, in fact, very much unlike the truth.
> 
> When this phrase is used, it apparently incites the sense that "This couldn't be a lie, but much nearer to the truth". It isn't apparently recognizable as double-negative when someone(even with much familiarity with English speaking/listening) hears this for the first time, but innocently could interpret just the opposite that is mentioned above in quotes.
> 
> 
> 

> 
> What could be the reason that these kinda "dubious" double-negatives came to be and widely used despite their inherent nature of inspiring "reverse" than what is intended meaning by the speaker ?
> 
> 
> 

I think that a more accurate statement would be:

> 
> When this phrase is used, I get the sense that "This couldn't be a lie, but much nearer to the truth". I didn't recognize it as double-negative when I (even with much familiarity with English speaking/listening) heard this for the first time, but innocently interpreted it just the opposite that is mentioned above in quotes.
> 
> 
> 

> 
> What could be the reason that these kinda "dubious" double-negatives came to be and widely used despite my understanding them the "reverse" of what is the intended meaning by the speaker?
> 
> 
> 

Unless you have some evidence that this is the general response, you shouldn't present your personal confusion as being an "inherent" property of the phrase. And the standard isn't whether a non-native speaker who has learned basic English is confused, it's whether a native speaker is. Language generally doesn't develop with ease of foreign speakers in mind.

You describe your incorrect interpretation as the "instinctive" understanding, but that "instinct" isn't necessarily a natural, objective way of looking at language, rather than an arbitrary pattern that you are so used to that it seems "normal". Native language acquisition involves wiring the brain to think in certain ways, and it's natural for those ways of thinking to feel universal, rather than particular to your linguistic community.

While it may take some thought when first seeing this to figure out what it means, it is pretty straight forward: it is the furthest from the truth that it can be. It is the most not-truth possible.

> 
> "This couldn't be anymore further/father than truth".
> 
> 
> 

It should be "any more", not "anymore".