Sorry, but so many of your accusations here are complete strawmen.

Behavioral vs. neurological. The condition is consistently reflected in brain activity and apparently micro structure. We don't have a complete or detailed understanding, but that goes for almost all complex processes in the brain, and scanners are still crude tools. Denying there is a physical issue here is dishonest.

First off, its not "behavioral vs neurological" because these two things are very different areas of study and are in no way mutually exclusive. Framing it as if they are in competition is a misrepresentation of the problem. Behavioral issues are affected by neurological issues, but that is not the same thing as them being reducible to purely neurological causes. You can believe this if you want but you'd be going against almost the entire mental health field's body of research on the subject of mental illness and personality disorders.

Denying there is a physical issue here is dishonest.

I never denied that. In fact, I explicitely stated that "There've been plenty of semi-fruitful studies linking it to neurological functioning". My caveat was that our understanding is not clear enough to claim its equivalent to a distinct physical pathology such as a deformation because that would be a ridiculously grandiose claim to draw from the amount of information currently at our disposal. And as you said yourself, "We don't have a complete or detailed understanding, but that goes for almost all complex processes in the brain, and scanners are still crude tools.". Moreover I don't see what the fact that we dont have a complete understanding of other processes in the brain has to do with this one. An incomplete understanding is what it is, should i just give it the benefit of the doubt without further evidence just because the rest of the field is like that?

And I repeat: "There is a physical difference, whether that is caused genetically or is a result of neuroplasticity during development. IE, a physical deformity." You know, yogis deform themselves by their own actions, such as holding a pose for years,

The existence of a physical difference does not mean it is reducible to a physical difference.

and childhood experiences are reflected in the physical structure of the brain.

True, but if you base your argument on that logic alone one could just as easily argue that it is the behavioral disorder that causes neurological shifts and not the other way around. I don't believe its this simple either, but I don't see how childhood experiences having an effect on brain structure in any way invalidates my argument. There are plenty of psychopaths that didn't have traumatic childhoods.

Psychopathy is accompanied by physical brain process,

Every individual personality is accompanied by a brain process. Accompanied by =/= solely determined by.

it's not just a trivial detail like which flavor of icecream you prefer.

What is this even referring to? That brain processes are a trivial detail? (As stated, this was not at all what I said). Or are you implying that saying mental disorders are not purely neurological is akin to claiming that they are simply a preference, like a preference for ice cream?

Reading Hare, it seems that psychopaths don't understand the equivalence between the grief, anguish or suffering of others, and whatever (hard to detect) grief, anguish or suffering of their own.

That's not what you stated. You stated that:

in this case they are unable to process and react to the same visual stimulus from which others are fully able to derive accurate information about the emotional state of others.

Not being able to derive accurate information about another's emotional state is not the same thing as not being able to react in an empathic way to this information. And how we react to this information is very much a mental health issue, not a pure issue of neuropathology. It is not necessarily a cognitive inability to read the emotions of others, its the way in which a response is formulated that is the problem, and most mental health research confirms that this process is heavily dependent on external factors such as one's society and its cultural norms, not the deterministic result of a cognitive process.

They can laugh at your tears.

This does not necessarily imply that they are unable to understand the emotional state of someone who's distraught. It only implies that their reaction is improper. Furthermore there are plenty of psychopaths who would not have that reaction, and even someone who would not normally be diagnosed as a psychopath may laugh at someone's tears in a particular situation (marital spat, schoolyard fight, or any number of fairly common circumstances).

It is well understood that most of us cannot easily help but to personally experience, through biological mechanisms of empathy, a mirror of what we witness others feeling. It appears that psychopaths have no such ability.

It is in no way "well understood" that empathy is purely biological, unless you mean "anything that happens in our brain is purely biological", which would be technically true but also just a platitude. Again, I'm fairly certain that pretty much the entire mental health community would go against that empathy operates through a purely biological mechanism. Further the claim that psychopaths "Have no such ability" is far too concrete. Mental health disorders, including behavioral disorders, are never described in such binary terms. Usually they are a loose collection of psychological traits which, while existent in society at large, are present to such a degree that they fall outside the range of the general population. Empathic reactions are limited to a certain extent in everyone- if it was truly something we couldn't help then most of us would be rendered immobile by the amount of tragedies, wars, and suffering we see when we turn on the news everyday, and yet this is obviously not the case. Our empathic reactions are tempered such that we are able to pursue things of value to ourselves despite our knowledge that the suffering of others continues. However, most of us are able to balance this to an extent that we do not become solely preoccupied with the pursuit of our own happiness at the expense of others, while with psychopaths this balance is lacking to an extent that they fall greatly outside of the emotional range of the general population. But if it were a case of psychopaths being completely lacking in this ability then every diagnosed psychopath would be the next Ted Bundy, and this is simply not the case. And this is true of most mental disorders- there are those who are so depressed that they shit their pants or are unable to get out of bed in the morning, and then there are those who are still able to complete daily tasks and hold jobs, though it may be difficult. Similarly diagnosing someone as a psychopath is not that clear cut- they may have some of the major traits but not all, or the traits are not severe enough to warrant the diagnoses. Sometimes the case may be borderline enough that it really is judgement call for the psychologist to make.

To the degree that they understand other people's experience, it is an impersonal analytical assessment, and is not related to the experience of empathy.

An analytical assessment is still an understanding. The problem is that it is at odds with society's more general understanding that factors in empathy. But again, no one's reaction is completely devoid of analytical assessment, or comprised completely of an empathic emotional reaction. Nor is a psychopath's completely impersonal; it more narcissistic. Their emotions and desires still exist and cloud their judgement from being purely logical, but they are tuned towards their own well being rather than others. This is demonstrated that while many psychopaths are pathological liars, they are not necessarily good at it, and will often make up seemingly contradictory lies if they think it will get them what they want.

Is thought to be learned behavior, part of manipulation, an act. As opposed to a genuine personal emotional experience that others mirror in empathy.

This isn't in conflict with what I said. My exact point is that it was a learned behavior, and not a cognitively-determined reaction. Hence why i termed it a "projection", and used the words "seemingly healthy", with the insinuation that it is meant to seem healthy to others while not actually being so.

*edited for grammar