I can relate to this. I am an INTJ. But as a psychology nerd and minoring in counseling, I don't think this is caused by MBIT, this seems to me to be related to attachment theory. I do think being an Fi rational predisposes you to this though. Here is why I think this happens. Having a low emotional/ social IQ and finding it difficult to learn fluency in emotional expression is a weakness that take work to fix. xNTJ's are passionate and when something or someone matters they give their all. But when that comes to emotional connection.... Well at a young age that means putting the raw emotional self into a relationship. So when that results in pain, even from say a parent going on a weekend vacation. The separation causes pain. Physical pain since you gave most of yourself to another who is not there so now you are two pieces. The low fluency means that the young person cannot express the pain. And they don't have a way of releasing it. So it stays inside. As a result they build a wall and make sure their emotional self stays inside. They become self reliant, strong, and not easily touched. They use their rational sides mostly to try and deal with the emotional, hence the scathing sarcasm and murderous thoughts, they are emotional release. This is why rationals have a problem handling another's emotion. They would need to remove walls and connect to provide empathy and support. So they either freakout or develop a procedure ("ie, tears 1 find out good or bad, 2 if bad provide chocolate, napkins and listen nodding and making sympathetic noises, 3 care physically for them. Ie clean, cook...) To avoid vulnerability.
Though this is very helpful in dealing with the masses and the acquaintance, it does not allow the individual to connect, often results in isolation, and escapism (tumble connection, gaming, books, passions) they can almost be obsessive because then they don't notice the isolation and hard feelings.
That is why writing g about a distant loved one will hit you harder then not seeing them for 6 months. You have built strong enough walls to contain emotion but when forced to look at it, hits you.
As a father I notice how vulnerable my toddler is to emotional upset. In talking with my mother I found out I was the same way. Easily affected. But I never knew how to express it so I would either get angry or shut down. I was showing myself as an intj from that age as well. My son is showing all the cognitive functions of an xNTJ as well. But knowing now what I needed I am trying my best to teach him emotional literacy.
As I go through counseling and being married to an INFJ, have begun to learn emotional literacy and raise my emotional IQ. I have learnt to only give parts of myself into a relationship that equal to the importance of the relationship. Parts that can grow back quickly. Think of it as donating a bit of blood. It grows back quick and it you Dont give a lot there is no pain felt when it is gone. But you can then build genuine connection and loose the isolation.
When I am separated from my wife or close relations, for a time (like a week climbing trip) I feel the physical pain in my chest and elsewhere but I can name it and release it, (often in notes I write and give to her when I get home) it never becomes something I regret. Because I have been taught how to deal with emotion.
Just like some find math easy and not English, so it is with emotion and rational thinking. Some find one easy some another xNTJ are predispose to the rational and struggle in the emotion. But I can and I am learning and changing.
MBTI is about showing your strengths and weaknesses so you can understand other, and your self, then learn about and improve your weakness.
So you are not stuck like this... change. To fix the callus so you can fill the core need of humanity to be connected to another. Not everyone but at least one. Learn to open up and to handle pain. Handled properly you will still be strong and ineffective because you process it, and release it so you can then function and love them more.