A few reasons in addition to what others have added.
1) I have yet to see an instance where they have been proven to be repeatable (as in the same person scores as the same type consistently).
2) All of it assumes that the person taking the test is telling you what they really are, and not what they think you want to hear. Some tests do try to ask the same question in multiple ways to trip someone up, but anyone who is paying attention can get past that. So now you're not testing their personality, you're testing their projection of a personality.
the underlying assertion is that attempts to formalize a nomenclature for personality are based on false premises; and more importantly, are not meaningful predictors of behavior (e.g. success in a given role/industry/whatever).
There is a footnote here where the question is not "are these measuring objective qualities" but "are the answers people give, to the same test, correlated strongly with things we are interested in." Such as succeeding at the "corporate rat race."
Related rabbit hole:
The meaningful argument in favor of IQ tests is this: not that what they are measuring is strongly correlated with "intelligence" however defined; but rather, that performance on these tests is correlated with things employers are interested in.
Supeficially that would include "being good at taking standardized tests" but success is I imagine more correlated with "knowing how to play the game of taking these tests, and, how to 'game' them to get the best results regardless of knowledge,"
not to mention problematic things such as "having internalized and being fluent in the dominant cultural language and its knowledge base."
1) I have yet to see an instance where they have been proven to be repeatable (as in the same person scores as the same type consistently).
2) All of it assumes that the person taking the test is telling you what they really are, and not what they think you want to hear. Some tests do try to ask the same question in multiple ways to trip someone up, but anyone who is paying attention can get past that. So now you're not testing their personality, you're testing their projection of a personality.