I'm probably not INTP, but i will butt in regarding an aspect of the discussed phenomena.
I like BAP's input and train of thought.
At the risk of fuelling your want to feel intelligent, percieving a lot of your failures and limitations puts you ahead of most "Mensa area'ish" people in regards to perceptiveness and ability to improve your own cognitive foundations. To take a directly conscious part in shaping your own mental development.
As BAP said, metacognitive ability is a great tool to use in order to find out how to use the tools one has.
One can even modify them.
You might eventually also find yourself increasingly figuring out how to utilize this self-scrutinizing ability to understand how to use the emotional tools available to you so that you can build a more stable and content sense of self without sacrificing your ability to percieve limitations and flaws in your own thinking.
A trick I used to use was to alter my mindstate in the way necessary to start to focus not on the failures of the inconsistency or incompleteness of my previous utterings or thoughts, but to focus on that percieving them now made my thoughts more solid and better. To not focus on the idea of the past as a painting that in hindsight was ugly, but at my mind as a painting in progress that is becoming progressively more fleshed out, strong and reliable.
Illustrating (there are probably other ways to look at it too):
¤1
Past Thoughts : Thoughts after having recognized mistake = less than 1
Suboptimal, lacking. I failed? I failed the test. I failed. I did bad. I am shit. I want to die.
¤2
New thoughts : Past Thoughts = more than 1
Improvement, increase. Recognizing past mistake gives a good feeling. I have improved. Yay me.
~~~~
The school system's test system encourages people to adopt a type 1 system of feeling. It doesn't matter if you improved, what matters is that you failed and you can never take that failure back and you are bad. Others didn't fail then and so you are a failure compared to them. Things not being about self-cultivation, but about every "performance" being stellar.
It's a constant lamenting about the past self not being as good as the present self. Instead of running back to those friends and enthusiastically being like "hey, I just realized this is a more correct view than the one I previously shared and here's why", one will almost not want to talk with them about it because one is ashamed. Rather than fuelling the joy interpersonal relationships, it drains it.
It can also be transferred to comparing the imperfect now against an imagined perfect/better possible future self, yielding again a less-than-1 number. Flip it on its head you get a more than 1 number and a good feeling, even though its the same thought, mathematically.
@Trivial I'm not sure if this is useful for your or not, as we are not the same person, but getting results on proper fluid intelligence tests did not lay anything to rest for me. It shifted some of the focus/stress in the internal struggle into whether I could harness my potential or not and if my will was strong enough. I am probably Ni dom at the moment, though. So percieved strength of will might have more likelihood to be central to my identity than it would be for you by default.
Lastly,