Why is it so unreliable to type a person with the Jungian dichotomies alone? Because it can be very hard to find out a person't preferences. That's the reason why MBTI typings are worth nothing.
Using Reinin dichotomies, we can easily see why dichotomous typing it is so difficult. Some examples:
People who tell a lot of stories are not necessarily extraverts. They might be introverted*declaring instead...
People who seem to have an analytical mind are not necessarily logical. They might be ethical*static instead...
People who seem to be unemotional are not necessarily logical. They might be ethical*serious instead...
More examples:
Focus on wellbeing of own group: Ethical XOR Logical*Aristocratic
Think about the future: Rational XOR Irrational*Farsighted
Focus on goals: Rational XOR Irrational*Strategic
and so on, and so forth...
This might also be a good explanation for strange typings in MBTI: Those MBTI practicioners seem to believe that people who focus on goals are always Judging, they don't consider Perceiving*Strategic for them.
Dichotomus typing is not a bad method - but you have to use all the 15 dichotomies then...