Jungian-based personality typology like the MBTI aren't totally without merit... but their biggest pitfalls is what people do with them or think it means, reducing them to being essentially a horoscope.
That said, personality typing/inventory is also not totally sound either, and some of it's issues are internal within the basis of the typing itself and their own official descriptions that are borderline-horoscope, as well as being pseudoscientific in much of it's approach and testing implementation.
For example, look at how many people don't even understand what introversion is. Many still assume it's shyness or social anxiety.
Go to any dumb online group for personality types and it's nothing but psychosomatic-induced social anxiety (in "introvert groups"), and all the memes are about social anxiety, and a lot of their posts are self-fulfilling prophecy nonsense and a bunch of circle-jerking about how special they are, and a bunch of people making themselves ridiculously exaggerated caricatures of what their results say they should be. "OMG, that's SUCH an ENFP thing to do!" or "I don't think you're 1 wing 9, you're more like a 2 wing 5" (Enneagram). Personality typology doesn't translate directly to external behavior, it's strictly internal tendencies and more interpersonal style that sometimes influences (but not necessarily dictates) external behavior.
While personality typing as a whole is theoretical, the only aspect of any of them that has consistency and a clear basis is introversion vs extroversion, neither of which is what people often make them out to be, and also isn't a dichotomy where you're either one or the other, but more like a sliding scale where most are in the middle. You cannot get to know a person and accurately guess their personality typology, to include just determining introversion and extroversion.
The Big Five personality inventory has a little more merit to it, but that also has problems like many others. Nobody actually studying the psychology of personality can even agree beyond introversion and extroversion, what the various other aspects, qualities, dimensions, whatever would even be, and there's no agreement how to properly measure them. Hell for that matter, there's no agreement to even how to define "personality" itself (in the context of psychology).
For what it's worth, any time I've done one of these, I've always been pegged as an INTJ.