A Theory of Autism
Consider a child with congenital paraplegia or quadriplegia, say severe cerebral palsy or spinal muscular atrophy. They're never going to understand and be able to empathize with the feeling of accomplishment of a factory worker assembling some complex thing for a big paying contract. Similarly, that same factory worker can't understand and be able to empathize with the difficulties of the troubled movement or even inability to move certain limbs. You can show support and care and consideration, but you can't actually empathize because fundamentally you don't know what it feels like. You've had couples therapy where this was a problem and you have to walk them through each others perspectives and feelings and why it led to each persons actions. You can get them to eventually understand, but still not empathize.
One of the neurological findings was damage to the vagus nerve. Aside from controlling the bowels, explaining constipation issues and potentially even the higher rates of depression (most serotonin is actually produced in the bowels and serves non-mental-status functions), it also controls the facial muscles. A very large amount of autists are described as having very flat or otherwise inappropriate facial affect. The perspective of psychologists like Baren-Cohen was that this indicated a lack of understanding of appropriate emotional response. I would argue that rather, with known neurological issues, this is described far better as a localized palsy; localized, instead of general, numbness and difficulty of motion. It's not that the autist doesn't know how to affect, but rather, they beleive to be and aren't. I've tried in the past, sitting in front of the mirror, to get an obvious emotional display out of my face and I just can't. I've tried this with others and it's just never right. Every time, either myself or the other autist says they feel like they're expressing --they can feel the contractions of the appropriate parts of the face-- but there just isn't movement. This is the exact same sign visible with other types of paralysis. With this in mind, you'd expect there to be an increased tollerance to pain, and I can say from experience I'm far less bothered by a punch to the face than most people. It's not just adrenaline, I don't even feel much pain after, despite bruises.
A more modern hypothesis of empathy that's been proposed fits nicely together with the double-empathy problem: the idea that empathy is actually a very personal thing, and empathizing with someone is strictly saying "hey, you're like me". With these ideas in mind, if you grew up being unable to move your face, you're going to be expressing yourself in other ways. Since we know in child development that until theory of mind develops, everything has to be viewed strictly through your own lense, you'd then expect an autist to look for body language and other social cues outside of the face. These are actually easily found, and far less of a focus for people trying to hide their true intentions, partially leading to social difficulties.
Furthermore however are the sensory problems found with the condition. While it's often stated that only a subset of autistic experience this problem, I think it might be more universal. Most of the research into this has the obvious deficiency in asking people if they experience any sensory disturbences. Since you do not know how other people sense the world, how do you know if your sensory experiences are any different from others? I did not know the way I feel certain things was different until I was 27, when a roomate asked me why I responded a certain way when I touched cotton. I thought everyone had an almost nails-on-chalkboard experience when touching it, and put up with it just like I did. ASAN has tackled identifying this differently and so far is finding almost every single autistic member can identify at least one of these. In my own experiences I've been able to find numerous as well. Like a "stubborn autistic child" who "refused to brush his teeth". Used a different type of brush and kept his other hand under running water and within a week he was brushing his teeth fine on his own, no prompting. When your very framework for experiencing the world, your senses, operate differently, and there's very few ways to effectively communicate that, as well as no strictly observational way to identify that in another individual, of course the two parties would empathize differently. And when the other party can't see the disability, of course they're going to expect everything to fit within nonautistic expectations. The sensory discrepencies largely follow a pattern in how they are described: "overwhelming", "painful", "disturbing", "like I'm in physical danger". There are atypically positive ones too, but these rarely contribute to "behavioral problems". Aside from the facial palsy, a large number of autists, myself included, describe discomfort or even pain looking at another persons face. With recognition of sensory issues in mind, and the incredible density of communication, and therefore sensory stimuli, localized in the face, it's then very unsurprising this would be a common complaint among autists.
Prior to fifteen years ago, the majority of autism research was funneled through the lense that Baren-Cohen and Autism Speaks set up, and so most of the research was directed towards behavioral corrections through things like shock collar training (I wish I was kidding, this didn't stop until it was made illegal in 2017), ABA despite no significant reports of success, and... a huge corpus of research and resources on support networks for the caretakers. Of course, you'd expect behavioral correction techniques to fail if it wasn't a behavioral problem. These approaches for trying to get a quadrepelgic to walk would rightfully get you rediculed and your license revoked. Very little existed for the afflicted. Left to address this on your own, what do you do? One option is to heed common advice. Treat others the way you want to be treated. Having to deal with all this unpleasant barrage of sensory stimulation, especially not aware that others don't experience that, is extremely unpleasant, sometimes even migrane or vomit inducing. Bypassing that is more pleasant. So if I want to be treated in a way that accomodates this better, and I'm supposed to treat others the way I want to be treated, then you'd naturally expect the autist to develop a very shallow personality, being very blunt and direct and transparent. Or, as it was historically put: crude, lacking tact, and social awareness. Other ways of dealing with it are of course to withdrawl from the sensory assault that is socialization, schizoid style. You see exactly this especially in aspergers, where it's been likened to schizoid personality disorder. Or you give up entirely and kill yourself; an extremely common outcome.