Note: I have invalided a lot of what I say in this article, but I am keeping it here for documentation of my earlier thinking. Please read my more recent article, "Typology as a Language, or Why Loops are a Symptom of a Larger Problem", to obtain my more current beliefs.
I am sure many can recall an event by which a typing on the site has been done in such that someone claims that a figure must be, say INFP because of an Fi+Si loop. This person however, has not explained whether or not the INFP in question actually uses Ne. This comment is likely to have been given multiple upvotes, maybe even in the double-digits. Along with grips, this is likely one of the most fallacious non-arguments on PDB, and must be discarded as an acceptable typing method. Below, I will make various counterarguments to the idea of loops, and while the ideas below cannot be taken as a whole, any combination of these counterarguments should be enough to dismantle the idea altogether.
For something to be, there must be a justification. For loops and grips, that justification does not exist. Why do people argue for loops and grips? Under what basis does the legitimacy of loops or grips equate with the mbti theory in itself? I cannot imagine how these kind of things originated, but there is certainly no primary source that verifies the existence of these pseudo-theories. Jung, Myers, Briggs, or even Augustinavičiūtė do not have any documents or text in relation to loops. To create a good analogy, the mere idea of loops has the same level of efficacy and legitimacy as something like CS Joseph's theory, DaveSuperPower's theory, or any other user-made theory that doesn't line up with what has been set in stone. Your tumblr article or /r/mbti post is not a justification for why a character is a certain type.
Loops in itself bastardizes the cognitive function theory in many unprecedented ways. If say, you are to type someone as INFP by the Harold Grant stack theory (which is what everyone uses anyway) , you are typing by Fi-Ne-Si-Te in that priority. If you argue that a character is Fi-Si-??-?? (no one ever answers what a looped stack even looks like), then you are no longer arguing for INFP. You are arguing for something nonsensical, as no type has a stack of Fi-Si-??-??. While this notion ignores the complications and problems of function stack theory, I am merely playing along to what society deems as 'normal' in terms of typing by "mbti", and the double standards that are enforced by promoting pseudo-theory such as loops.
Another major problem is what loops are used to justify. In my previous example, I noted that people use "Fi+Si" to justify INFP, but that should be strange, as you are using a feeling and sensing function to defend an...intuitive typing? That seems off, doesn't it? After all, if you observe any figure, and the most noticeable traits are their feeling and sensing functions, you would try to instead justify some kind of SF typing, no? This is especially the case if one is to argue their Si is more prevalent than their supposed intuitive function, Ne. Perhaps this is the so-called 'intuitive bias' these kind of people speak of. Or maybe, just maybe, these characters are just a sensing type, whether ISFP or something else.
Food for thought: What is stopping me from reversing the Fi and Si, and instead arguing for Si+Fi, ISTJ? This is especially the case if the supposed priority for these 2 functions are too similar to differentiate. The lack of substance and cohesion to the idea of loops leads to these kind of possibilities, as there is nothing to really go against the obvious question: why not?
Grips are not as bad as loops because they focus on the inferior function, so it does not try to force a typing with an utterly non-coherent stack. At least, they admit that the stack is something like (ex: INTJ): Ni-??-??-Se. But the problem is still evident: you have not proven INFJ or INTJ as a distinct answer, but merely Ni dom. Sometimes these people bring this up in a comment without a vote, but then I ask, what is the purpose of writing the comment? It acts as a red herring to those who legitimately have reasoning to correlate to a specific, distinct type. Mental health is too subjective to judge certain figures, especially villains, who are always called unhealthy when it is convenient. This is despite the notion that most villains are 'healthy' in terms of their ability to function in a precise manner, it is merely a moral conflict between the typist and the subject to create this illusion of ailment. Grips are a useless idea to bring up that, like loops, have no real reason to be mentioned or even exist.
This article is not to argue that every single subject fits their type in an exact order; every INFP is Fi-Ne-Si-Te. I have my own critiques of the cognitive function system, but in a sense we are supposed to adhere to a strange mbti 'social contract'. We all agreed informally as a collective that the Harold Grant stack typing method is the preferred method of determining someone's mbti type. To skirt around this and use pseudo-theory such as loops or grips, is unsatisfactory and demonstrative of one's lack of creativity in arguing a subject's type. I feel like after going through these arguments and possibilities within the mind, it requires massive cognitive dissonance to continue justifying loops and grips in any kind of serious manner.