If you dig a little deeper into the foundation of analytical psychology, you might be surprised. Carl Jung popularized the terms Extravert and Introvert, and there have been at least 2 studies (that I know of) in neuroscience showing that dichotomy to exist, physically in the brain.
I'm hyperrational, started 2 successful companies, majored in CS, atheist, don't believe in horoscopes, or any bullshit for that matter, but do believe not all brains process information in the same way.
Now to say the MBTI test does not have some validity issues, would be delusional. But on the other hand, only an arrogant fool, would conclude that therefore there is a fundamental problem with the theory.
For example, if I construct a test that asks 500 people (assuming highly randomized sample) if they like sugar. And 250 people say "yes". One cannot conclude 50% of people like sugar.
The best you can hope to conclude is that 50% of people, self report as "liking sugar".
So what this means is that the test makes some flawed assumptions: eg
1. people are honest (consciously and/or subconsciously)
2. people know themselves enough, to give accurate responses
There may be more, but those appear to be the major flaws accounting for validity and reliability issues (engineering synonyms are, accuracy and precision). It is also plausible, that these challenges are not insurmountable.