Tell a kid 100x that they're bad at maths and eventually they'll believe it, and never want to touch a maths book.
I agree with your sentiment, but sometimes people do have aptitudes and biases whether or not someone points them out.
In my case, I actually AM bad at math. Specifically, I'm bad at rote. I do very well with problem solving, so long as I can use whatever resources are available to me to do so. Problem solving within the constraints of rote is extremely difficult for me, as my mind tends to ignore the rote if there is a path of less resistance.
It might encourage or discourage someone... then again it might piss them off and prove you wrong despite their inherent talents or handicaps.
Tell a person they're INFJ (or whatever) and maybe they believe it too....? Even if they're not, maybe their belief will subconsciously compel them to express those parts of their personality that are more INFJ ish and suppress those parts which don't fit with their mental image of who they are.
Again, I agree with this sentiment, humans are likely to make self identifications... usually based on observations.
However, I've noticed that INFJs in particular are predisposed to questioning their type, even when everyone around them insists they are INFJs. We seem to ask the question, "Do I really fit this?" more often than most. This implies that we're less susceptible to self identification than seeking the truth. (And yes, I understand how ironic that statement is, hehe.)
IMO your perception of who you are GREATLY if not entirely controls what you actually act as and do. So those parts of the profile which actually aren't very positive or beneficial, eg. that INFJs can't logically explain how they're coming to decisions, are doing you more harm than good, because you might take it as an acceptable limit - just one part of your indelible personality type. And the longer you identify with any particular profile, the stronger would be the association between it and what you're willing (perhaps even able??) to do.
So in a way, we might be constraining ourselves to behave in a certain way because of what type we believe ourselves to be.
I look at type descriptions as commonality, never rules.
I never see "INFJs can't do this or that..." I see "INFJs are less inclined to..." The opposite is also true. I never see "INFJs always do..." I see "INFJs are inclined to..."
The reason for this is that personality type is not dictated by the strength of our functions, but by our preferences with our functions when they come into conflict. It is common for INFJs to have a less developed Te due to the nature of the type's preferences, however some INFJs have an extremely well developed Te due to life experiences. Niether of these conditions affect whether or not the INFJ prefers Ni and Fe over Te, even if their Te is stronger than their Ni and Fe combined.
Personality is a function of preferences. Intelligence is a function of capacity. They are easy to confuse, especially with self identification. Cognition preference is inherent. Self opinion doesn't affect it much. Self opinion affects choices once cognition is applied.
For example, someone might be an INTP who thinks they are an INFJ due to test results. The INTP mind would make decisions and process information based on how it understands things to work (Ti) and the possibilities it sees (Ne)... which could then make decisions based on the possibilities of how it understands the INFJ personality to work and seek to conform to those parameters. This would be made easier if the INTP had a well developed Fe and Si, as the INTP could 'lean on' their Fe... consciously tapping it to support their Ti, and use their Si and Ne in tandem to approximate Ni to support how their Ti understands Ni to work. They'd be consciously making choices with their inherent cognitive functions to simulate something that they are not.
In other words, anyone could convince themselves of anything, regardless of whether or not it is accurate, which can be a very beneficial thing if the end result is beneficial. Choosing to believe you are a truly good person will have you acting like one, even if you're not, so the end result is beneficial. The only problem with this appraoch is that at some point reality and projection are going to come into conflict and cause problems.
Just something to think about~
It is always good to think, especially about these sorts of things.