Could this points of difficulties really be considered part of the "core self" once they are overcome? What if instead of math or psychology or particle physics, this body of knowledge was "ethics", "relationship know how", "dealing with anxieties", and so on, and the education program was... Life itself. Would the hiccups be considered part of the core self then?
I would say yes - if you have to learn "dealing with anxieties" in the first place, then those anxieties are likely to always be there... maybe more or less, but although you have learned to overcome them, when you go do something different, learn something different, you are always going to run into a point where your anxieties threaten to derail you.. they may not win, because you have figured out how to manage them, but they will always be there.
If you struggle with learning when someone's talking at you, without being able to interact, then you may eventually figure out you have to write things down, and then get a friend to talk you through it later, or something. Once you've figured that out, and implemented that, your performance improves, and you no longer appear to be struggling - but that doesn't mean the initial hiccup has gone away, it just means you are working around it.
It's like performers who have a fear of being on stage, in the public eye... you'd never know it from their performances, but every time, before they get on stage, they have to steel themselves, trick themselves into thinking 'it's not so bad', bite the bullet and just go for it. That doesn't just go away once they've learned how to push past it. It might get a little easier, or their methods for dragging themselves up their get more effective, but they will never be that person who can breeze up their effortlessly without sweating a few bullets first.
Of course, that being said, there are certainly some superficial 'habits' which are learned behaviours that are certainly not static, and people can overcome bad ones and learn good ones, but I don't think that's what we're talking about here.
Anyway, if this is besides the topic for you, that is perfectly understandable, you are currently in an INFJ/ENTP relationship so you can speak better to the benefits of one. It is personally relevant for me because it is the main obstacle to considering a relationship with someone who thinks like that, and it's a problem on my mind because rejecting relationship opportunities with people I have extremely good chemistry with is... Not fun. That's clearly not the case for all ENTPs, was not the case for me in the past prior to figuring this out, and who knows, it might not be the case for me in the future.
Ah, fair enough, I was just pointing out that on the surface it is a debate about the self, which although informative, is not quite relevant to the topic at hand - but if we can bring it back to the relationship being discussed, then certainly.
But to that I would say: I don't think type theory is a particularly good indicator of relationship success or otherwise. To limit a relationship with someone because of their type would be closing yourself off to a lot of the joy and self-education that exists in getting to know another person, compatible or not.
Firstly, almost every type is going to have habits that annoy you, ways of thinking that baffle you, manners that rub you the wrong way, whatever. Every
person has their flaws and downsides. Many with nothing to do with type. There's no getting away from that.
But every 'flaw' also comes in a sliding scale from extreme to minor. Using INFJs as an example and going back to your initial comment, since that's an easy example on hand, if you are to criticise their action, their reaction could be anywhere from: "OMG Why are you always so mean to me! You obviously don't love me anymore and think I'm an awful person and I'm going to curl up in a ball and sob until you apologise!" anywhere to "Well, I'm doing this action because of <explanation of some reason of self>, but I can see it bothers you so I'll try to be better at that in future, or maybe we can figure out some way inbetween."
Naturally, the former would be very difficult for
any partner to deal with, and is likely to get very old very quickly. The latter would be something you could work with, take steps together to resolve the point of contention - and thus though it might bother you, it can be managed. (And most of us are somewhere in between those two extremes, I'll grant!). Yet on paper, both are INFJs, they would both agree they have the same flaw.
Anyway really it's not about finding someone that doesn't bother you - it's about finding someone that bothers you in ways that doesn't have you tearing your hair out from stress or losing sleep at night from worries. And where the good sides of the relationship more than balance out the bad. Turning someone with whom you have great chemistry down because of a theoretical aspect of their type that
might bother you seems... unfair.
While I'm not advocating to charge into a relationship with anyone with a spark of chemistry, all you can do is evaluate the
person you are considering, not just their type. Type is just a tool we use to better understand those people who are in our lives and enrich our existing relationships. It shouldn't be a barrier.
(Oops, and sorry for the wall of text, so much for wanting to rein things in

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I can't speak for your friend, but for me, when my friend tell me that she agrees, I always think "does she says this because I annoy her or because she thinks the same?" and secondly "do we think the same because of the same reason ?"
Oh yes, he's definitely said the former to me before!
Actually, it's more important for me to debate than to convince. I'm not an INTJ who wants that the point is settled. I like debating, and I am not searching to tell you you are wrong. I want to understand you, why you are thinking this. Telling me you are right is good for INTJ (more ISTJ, I think, because an INTJ will think you are telling this because you don't want to listen), I WANT you not the agree with me, so that we can debate ! A DEBATE PLEASE ! Of course this sounds like he wanting to convince you. This is the point of a debate, trying to convince. But the important part is convincing, not being "right" (considering that truth exists, which can be debated, anyway

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You are trying to be convincing, but you don't want to convince!
I do enjoy a debate too, but my enthusiasm just doesn't always seem to last quite as long as yours. And what I don't understand is when one party 'gives up', either through agreeing, or agreeing to disagree, doesn't seem to matter, you guys won't let the matter lie... the debate has to continue, even if it's only one sided!
(For me if I'm not being argued against/new material to react to provided I find I will rapidly run out of things to say and taper off into silence even in the middle of my argument.)