A couple of events lately have had me thinking about the Myers-Briggs personality thing again, and specifically about some of the quirks of my own INTP type.
I want to preface this by saying that I'm trying to be a little bit self-aware as I write here. I'm going to present INTPs according to the way that (I think) they naturally view the world - the things that they'd say, "Of course this is true," if they didn't really stop to think. I'm not actually claiming that this is the way the world works, or that it's necessarily the best way to view the world - but this is what it feels like from the inside, when you're in the zone of your own personality and not seeing the alternatives. I'm also painting a little bit of a rosy picture of INTP motivations - they're sometimes driven by spite or pettiness or what-have-you like anyone else, but this is how they think when they're generally trying to be good people.
Anyway.
One of the big things for an INTP - one of the central, defining qualities - is that being right is very important.
I don't mean that it's very important that you, personally, are never wrong, or that you convince everyone else you're right - although these are, I think, the ways that it's usually perceived (and more on this later). What's important is that people, as broadly as possible, believe true things that match reality. As a necessary prelude to that, it's important that people think in the right ways.
See, to an INTP, it's entirely possible to have feelings or beliefs that are wrong or ill-founded - and in consequence, these are feelings/beliefs that one shouldn't hold. Now, to an extent, I think we'd all agree with that. If Bob brings Jim a delicious cake with the best intentions, and Jim gets furious at him, Jim had the wrong reaction* - not "wrong" in the moral sense, maybe, but wrong in the sense of, "There are reactions that more accurately fit with what is really true." If everyone could just figure that out and stick to it, hey, all problems solved - and while the INTP knows that's an impossible dream, he looks on it as an ideal to shoot for. The closer the world gets to that, the more it is predictable and safe; the further the world strays, the more life becomes a random, incomprehensible terror.
Now, a reaction can be wrong and still be understandable - maybe Jim had a really terrible day and would blow up at anything, or maybe he's on a diet and just keeps getting junk food thrown at him. Likewise, a reaction can be wrong and seem to be correct based on what you know at the time - maybe Jim (mistakenly) thinks Bob is trying to poison him, and so from his perspective this is the right decision! Again, "wrong" is not a moral judgement - just question of "From the perspective of an all-knowing observer, is this a justified reaction, or not?"
(I'm using an emotional reaction as my example here, but I could construct an identical example where Jim reaches a wrong belief, maybe for understandable reasons or based on preexisting false beliefs. Everything still applies.)
And an INTP is (hopefully) going to acknowledge that everybody makes wrong judgments. People are neither infallible nor omniscient; even someone who is very concerned about thinking the right way is going to sometimes flip out or work from wrong beliefs. After all, the INTP himself certainly does! Thinking about things the wrong way is bad, maybe, but completely unavoidable.
And this, to him, makes management of wrong-thinking absolutely essential. To leave someone with wrong ways of thinking is... maybe not criminal, but not far short of it: it's abandoning him to keep thinking wrong things, which is just going to make life worse for everyone, especially the wrong-thinking person! You'd have to really not care about someone to leave them in that kind of state without at least trying to help.
So to an INTP, the first natural duty of loyalty to a friend is to help them see when they're thinking wrongly. Done helpfully, it is a mark of affection and care that says, "I want life to be easier for you. I want to help you eliminate this thing that is causing you problems."
This... has interesting interactions when applied to personality types that view, say, personal support and affirmation as the first duties of a friend. An INTP isn't going to affirm you if he believes you're thinking about things wrongly; as far as he's concerned, that's like saying, "Yeah! Go drive off that cliff. I believe in you." That's not the action of a friend! No, what he needs to do is to stop you, first, to help you fix whatever mistaken thought is pushing in this direction, and then - once you're thinking correctly! - to affirm your new, better direction.
It is somewhat mystifying when these helpful pointers on "what I think you're doing wrong" are greeted with irritation.
See, it's not true that an INTP believes that he has no emotions, or that he thinks his reactions are always logical. (He may, in a moment, claim to be calm or logical, but on reflection most INTPs will admit that they aren't always this way.) Many INTPs will readily admit that they're very aware of having emotional reactions - those are the things they have to struggle to suppress in order to keep seeing the world The Right Way. Again, the ideal is important and worth shooting for: the closer one can come to perfect reasonableness, the better the reaction and the smoother the course of life. It baffles, then, when others seem to view emotion as something with a relevant and proper role in interpretive thought. Don't they know that emotion interferes with fair-minded assessment? Aren't they concerned that it might lead them to think about things wrongly? Surely they must be - so why aren't they fighting to level out their emotions, like the INTP?
Conclusions probably vary by INTP. Probably the most common one is that non-INTPs are simply lazy - they know that emotion is unhelpful and simply don't care about the INTP enough to push it away for the duration of the discussion. Claims that the emotion is important - that it may, in fact, be the point of the discussion - are obviously impossible.
One of the lowest-level (and most common) ways that this sense of the world plays out for me is as a drive to point out when people aren't considering enough perspectives.
For instance: Jim, having just gotten his cake, runs off to talk to INTP Ike. He complains about his day - and Ike, having had bad days before, genuinely sympathizes. He talks about how upset he was at getting the cake - and maybe Ike sees where he's coming from still.
But Ike also sees that Bob probably wasn't meaning any harm - that Jim is, to his mind, thinking wrongly. So (helpfully!) he points this out - "Well, that's true, but Bob was probably trying to be nice." (Jim was unaware of that, right? If Jim hadn't overlooked it, surely he would be taking the rational choice of not being angry.) It isn't that Ike thinks Jim has no right to frustration - but if he's more frustrated than the situation warrants (to Ike), then someone needs to present Bob's side until Jim recognizes it and moderates back to a more justified level of irk.
Again, strangely enough, this attempt does not always have the desired effect.
So fairness is an absolutely critical part of the INTP perspective, because the Right Way is by definition fair, weighting all evidence as it deserves**. This applies even when there has, indeed, been some wrong done - because if you can be wronged and still respond in fairness, you are in all ways superior to your opponent. A reaction that's out of scale with the provoking cause may be worse than the original offense (because it's bigger!).
So an INTP prides himself on the degree to which he can match himself to objective reality. He'll be very quick to point out when he sees a failing in this respect; on the other hand, he's very slow to reject his own beliefs if they're pointed at. This does not mean he is opposed to the critique. Rather, an INTP views this kind of conversation as a stress test - a chance to see if his beliefs really do hold up. If he can defend them against all comers, it means he probably was thinking in the right way in the first place - so he'll fight hard to do so. If he can't, that's good - it means he's just improved his thinking by rejecting a bad old belief***. But this is only a valid process of refinement if he pushes for his own beliefs as hard as he can - if he could be convinced by a lesser standard, he might let in more error than he takes out. He assumes you're doing the same thing!
All this together leads to the perception, I think, that INTPs always think they know better than anyone else and will never change their minds about anything. It's partially true, to be sure. An INTP is very heavily focused on knowing the truth; whatever beliefs he has right now are the ones that have won every cage-match they've been in so far. Until they lose, he's going to assume they're also bigger and tougher than whatever the new competition is. If you want to convince him, you need to bring a bigger gorilla and hit those beliefs harder than they can hit back - maybe harder than they've ever been hit before.
As far as he's concerned, that's what friends are for.
* - This is another INTP trait: a theory that fails at any point is regarded as a bad theory. So you can disprove "All reactions are okay!" if you can find any case where they aren't.
** - If you want to drive an INTP absolutely up the wall, habitually treat some group unfairly - judge them by standards you don't apply to others, say. This makes a lot of political commentary somewhat infuriating to me. I cannot, for instance, listen to Sean Hannity for long without starting to froth at his failure to even realize that there exist alternate perspectives - and I largely agree with him.
*** - I can point to arguments I've had that I was sorry to see end inconclusively - I was really looking forward to getting pinned in the contradiction that I could almost see coming.