Why are some people still obsessed with the Myers-Briggs Type Indicator (MBTI) theory of personality, even though it has been thoroughly discredited by modern psychology?

Psychology is a very young and slightly sketchy field of study, and still very far from a hard science. Lots of theories which are useful to study, not so much hard fact. The "Big Five" model strikes me as a slight re-factoring of types. Two things bother me. First, the fifth factor was supposedly derived from statistical analysis of data. Given that the folk I have met who went into Psychology were, frankly, not very good at math ... this does not improve my level of confidence in the result. Statistics can be very tricky, and you can too easily find what you want, rather than what is there. Second, the added factor smells of running home to mother (or in this case Freud). That the positive side of the factor does not have a clear label, raises doubt. That the larger group believes in a theory is not proof of correctness. There are a lot of advances and really interesting observations made in the last couple of decades. One much-used tool is fMRI ... which is like opening the back of an old vacuum tube based television, and noticing which tubes are glowing most bright. Without question use of fMRI has advanced the study of Psychology by large strides. However, if you are acquainted with electronic circuits, you know that some of the most important circuits carry only tiny currents. Psychology will take another leap when experiment can measure the tiny currents, rather than just bulk currents visible to fMRI. My point here is that Psychology is a very young field, with a very long ways to go, and much that is accepted now may change. Understanding the human mind ranges between physical measures and metaphysics. To presume that a currently popular theory is the final truth ... is rather premature.

MBTi is a an instruments which predicts the "Preference" and not "Trait". This personality instruments truly guides you in understanding one's own preference and appreciate another person's preference leading to a better relationship, outlook, team work and decision making. The fact that every individual is unique and has several gifts which needs to compliment with others when working together can be demonstrated well with MBTi.

It hasn't been thoroughly discredited by science at all; if anything, modern brain scanning techniques are supporting it more than any current theory of psychology is disproving it. The science you're citing is misapplied to the MBTI: 1)  MBTI doesn't measure traits, it indicates preferences.  It doesn't measure how left-handed you are, it indicates if you are indeed left-handed, as an analogy.2) it is neither conceptually nor methodologically flawed.  Just because Jung's ideas aren't popular today, it does not mean that they were wrong.  Nor is his lack of modern scientific principles and an issue as long as the MBTI follows standard psychometric standards, which is does quite well, thank-you-very-much.3) The five factor model (OCEAN) is itself flawed and biased, despite its gold standard, towards the O-C-E-A-N sides, and it is supposed to be used to diagnose mental issues, not indicate normal personality typologies.  Nor should the OCEAN's Five ever be used in an employment situation, especially since the administrator is most likely NOT a practicing psychologist.4) Since it is a type indicator (i.e. sorter), not a trait measurement, it is necessarily bimodal (inverse bell curve), and is served best when the questions seek to force the middlin' responses.5) It has never been intended to measure job competence, EVER.  It measures job SATISFACTION.  It should never be used by an HR department as an entrance exam or interview battery.  It should not be used for team selection or promotion evaluation.  The MBTI asks how satisfied one is with one's position, and compiles those responses vis-a-vis type.  That's how suggested career choice tables are created.6) Lay people find value in the MBTI because it WORKS.  Each Type is distinct, and once one finds their Type, the hair on the back of your neck stands up and you feel like someone has been secretly watching you your whole life.  Only one Type profile will do that per person, if they are sure of their preferences.7) Science is not without its own biases, and your question obviously reveals that.

A lot of the bad press for mbti comes from people not bothering to go back and jung in the original. Try it. I hope you will find some truth in it. 1) MBTI tests are a really bad way of determining type since most people a) don't really know themselves and b) give incorrect answers because they want to conform to what they want to be like rather than what they are and c) the questions are stupid and don't allow for anything other than yes no or 1 to 5 kinds of answers. 2) go read the type descriptions and try to see where you fit if you really want to find yourself 3) of course it's not possible to put 6 billion people in 16 buckets. There are a great many outliers and exceptions. But do you really think the S vs N divide doesn't exist? I think it does. 4) what jung meant by introverted isn't the same as the normal English meaning of the word introvert. It is possible for an introverted person to  be an extrovert (English word).