Preface: I wrote this post partly to try and capture/demonstrate/introduce/explain a concept that I haven't found an existing explanation on that would match my mental model. And partly to clear up my own confusion about the topic and put my thoughts in more precise words.

So what this is post going to be about?
I guess I would put it like, "how a highly sensitive person sees words, and communication in general". An exploration of some hidden-complexity behind words that already exists, but that maybe we aren't that good at paying attention to.

I'll start this as a dialogue, with some imaginary person introducing thoughts that are partially-flawed, then exploring how they are flawed.

"Martin Luther King is a criminal!"

This is a misleading thing to say. Martin Luther King was a prisoner of conscience, arrested for breaking what he saw as unjust laws in the course of his civil rights work. If by criminal we mean 'anyone who has ever has broken a law', then yes, Martin Luther King is a criminal, but we'll have to concede he is a 'good kind of criminal'

"And what if I genuinely believe that breaking the law is always bad? That there is no such thing as 'a good kind of criminal'?"

Just to be clarify, I assume you don't actually think that, for example, jaywalking is as bad as murder?

"They are not equally bad, but they are both bad. Both of them are crimes, and both a jaywalker and a murderer are criminals"

This might be Fallacy of Gray? Stubbing my toe is bad. Extinction of the human species is bad. There is a reason we typically use different words for concepts with vastly different magnitudes. I wouldn't say that stubbing my toe is a 'catastrophe', or that the extinction of the human species is 'a bit of a downer'.

"You are being disingenuous. There are plenty of general, vast-encompassing concepts. A 'celestial object' can mean an asteriod, a planet, a galaxy, a nebula, or anything in between."

Perhaps it's more important to use specific rather then generic concepts when talking about political, "sensitive" or emotionally-charged topics? For example, the concept of "a person who has ever done anything bad, whether it's stealing a plastic bag or genocide" might be too muddled to be useful. Even if you don't intend it to, the lack of precision in the terminology you choose to use contributes to a confusing and misleading message.

"I don't think there is anything misleading about it! I am saying exactly what I mean to say."

'Anyone who has ever broken a law' and 'criminal' are two distinct concepts in people's mental maps. And I would claim there is a substantial difference between these two concepts, not a trivial one. A person who jaywalks, or who rides in a car without using a seatbelt wouldn't consider themselves a criminal, even if these actions do break the law.

It seems that you are claiming that since you believe that 'anyone who breaks the law is a criminal', and since people agree with you, you not doing anything underhanded by using that as an implicit point in favor of your argument. But people don't actually believe that, they only believe that they believe it. If they actually looked closely at how they used the word 'criminal', how they felt when they thought of the word, they might notice it meant something different to them than 'anyone who breaks the law'.

If we actually look at the mental models of you vs other people, the fact that Martin Luther King broke the law is not a controversial point or a source of disagreement. If you genuinely believe that 'everyone who ever has broken the law is a criminal not just in a literal/technical sense of the word, but in the sense of what emotional/mental image the word criminal evokes in us', then that is how your mental models differ and that is where your disagreement lies with other people.

If you actually were to express your disagreement with other people, having internalized the concepts we are discussing now, it might sound like something like this: 
'Crime is terrible, not matter how small. I strongly believe that anyone who breaks the law is a criminal, that if you break the law even in a trivial way you should see yourself as a criminal. I realize the word criminal as it used now means something different, but...'
(I don't know what you would say further because it seems to me at this point you would realize that what you saying doesn't really make sense. Either that, or my understanding of your mental model is lacking).

The point is, you would need to address the outlying examples, the non-central uses of the term "criminal", because it's there the disagreement between your and their mental models lies.

What you are doing wrong is trying to draw a hard boundary around a soft concept, then treating that boundary as the actual meaning of the concept rather than just an approximation.
Even if you define 'criminal' as a binary term, our brains won't actually treat it as such. By introducing the category 'criminal' , we will see some members of that category as more central and some as less central. We will attempt to draw general conclusions about the members of the category, then assume they apply to all/most members, perhaps to the point that the least typical members 'drop out' of the category. 
'Would you expect a jaywalker to rob a bank?'
'No, because jaywalkers aren't really criminals.'
This is correct reasoning. It would be less surprising if someone who has committed serious crimes decided to rob a bank, than if a jaywalker decided to rob a bank.

The reason that concepts in our brains often have soft boundaries is because similarity clusters in reality often have soft boundaries. If you've only seen tigers before, and see you a lion, it's probably wise to treat it as 'unusually-looking tiger' rather than 'not a tiger'.

So. Our brains, perhaps unsurpringly, do a decent job of slicing reality into concepts. Except slicing is not really the right word, because slicing implies clear boundaries. An 'electron cloud', a 'probability density plot' is a better metaphor, except instead of probability, the density of the cloud represents 'how much does the concept apply to this particular thing' or in more technical/biological terms something like 'pattern activation strength'.

If the word 'criminal' has two different meanings, how do we know which one we are talking about? Let's introduce some terms.
The definition-meaning of 'criminal' is 'a person who has committed a crime'.
The impression-meaning of 'criminal' is the concept, the mental model associated with the word criminal. What you actually think, feel, visualize when you consider the word criminal; the sum of all the associations to that word, both the very obvious ones and very very subtle ones.

The advantages of definitions are that they are precise. If 'criminal' means 'a person who has committed a crime', and if we know precisely what 'person' and 'crime' means, there is no ambiguity. And definitions are easy to communicate to other people, so we can all agree to use same ones, or easily clarify what we mean if we happen to use different definitions of the same word.
The disadvantages of definitions is that that is not how our brains actually process words. So the definition-meaning of a word is an approximation to the impression-meaning of a word. And, like with many approximations, and an approximation can be very useful for one purpose, and a very poor fit for another.

So if impression-meanings of words capture the our mental-models better then definition-models of words, and if the goal of communication is to transmit our mental-models, why are we not always using impression-meanings of words to communicate? Why not just let our mental models speak directly with each other?

I would say that this is indeed what we are doing, but unconscously. The conversion of concepts into words and words into concepts are not-fully-conscious processes, and some people may not even notice that the definition-meanings and impression-meaning of words are different. But I do believe that the algorithm that converts mental-models into words and vice versa does that primarily based on impression-meanings of words, not on definition-meanings.

If you are to effectively communicate on the impression-meaning level, the ability to consciously perceive impression-meaning of words is a very important skill.
How do you actually do it? I'll explain, but first, a metaphor.
Some people don't pay attention to the tone of their voice. Some might not even notice that they are shouting, even if someone points out to them that they are ("I'm not shouting!!").
You might teach them some words to say, some communication technique, but as long as the tone of their voice is unchanged, that would detract from they are saying. Their error is on a different layer of meaning.
But it might be possible to teach people to pay attention to the tone of voice, perhaps even more subtle variations of it. Not everyone would be equally good of it, but it theoretically is teachable.
(As an example, I've read of an experience of a man who had recieved that kind of help/lesson/training, then spontaneously noticed during an argument that his fist was clenched and that he was raising his voice, something he never consciously paid attention to before).

Here's how you bring the impression-meaning used in a conversation to your conscious attention.
Pay attention to the "tone" of the conversation.
Not just what someone is saying, but what does expressing it the way they do imply?
How does it feel to listen to this? What is happening inside my mind?
The more precisely you can "percieve", the subtler patterns you notice in yourself when processing information, and the finer differences in impression-meanings of phrasings you can tell apart.

Some examples of applying this skill (besides the "Martin Luther King is a criminal" example, on which I hopefully have made my point abundantly clear). 

"I’m sorry you feel offended"
"This seems to imply that I'm being oversensitive, rather than that you genuinely regret what you said. Would you please clarify what you mean?"

"So you fled from that situation?"
"To me, 'fleeing' seems to imply cowardice. 'Fleeing' has a negative connotation. There is nothing wrong with leaving an unsafe or unhealthy situation"

Some more observations:

• An impression-meaning carries a lot of more information that a definition-meaning (how many bits would it take to fully capture your brain's mental model of "tiger"? even if some information is offloaded to other mental models, such as "tail")
• This seems to imply that talking to with people whose impression-meanings of words match our own would allow for more effective communication (on topics where impression-meanings matter). This seems to be true (talking to friends, people who share our "headspace", people in the same subculture, people in the same community)
• Communication is a process that "normalizes" language, both in terms of definition-meanings and impression-meanings (albeit this might be a slow process). That is, I would expect communication between people to make their usage of language more similar to each other (or least, learn the difference in how the other person/group uses language).
• Communities, groups, subcultures can develop a differing use of language, including different meanings of words as well as entirely new words/terminology (a rather obvious observation in itself, but this applies on the "impression-meaning" level as well).

Perhaps it's not that useful to talk about definitions.
After all, most of us can explain what words (like "airplane", "ladder" or "fridge") mean, without having read it in a dictionary, or even if dictionaries never existed. And dictionaries mostly just describe the common ways we use these words.

I could simply say that a definition-meaning is what we think a word is supposed to mean, even though I'm not sure that's strictly true as well.
I could say "map and territory", when the territory is what a word actually means to you, and the map is what you think it means. It's probably not a great metaphor, since in this case both the map and the territory are in your head - but it does seem true to me, or at least approximately true.
If ask myself to describe what 'criminal' means, is the answer I get is 'a person who commits a crime'. While in the back of my mind I am aware it's not the 'full' meaning, it is a still a compact description that can be expressed in words, and it is a good enough approximation for many purposes.
I'm not sure if my understanding of the cognitive/neurological/biological reality is fully accurate. But I do think making the distiction between a 'compact description' and 'full model that is processed subconsciously and is only partly visible to our consciousness' is really useful. 

This is why tabooing works, by the way. We throw away a term that is somehow ambiguous, or has misleading connotations, and substitute it with what we actually mean. Simply saying, "I define 'criminal' to mean 'person who has broken the law'" is not good enough (well, it might work, but to lesser effect) - actually remove the word entirely, in order not to contaminate what you are saying with whatever meaning our brains already have attached to the tabooed word.
"Martin Luther King is a criminal!"
"Can you taboo 'criminal' and try again?"
"Well, I guess I mean that Martin Luther King did some bad things and we shouldn't treat him as someone to be admired"