MBTI is braindead pop-science which is based on the rantings of Jung. It was good for the time (when measuring people's skulls to determine their personality was popular) but has no place in modern science.
The biggest problem is, it's deliberately polarising. Jung thought there were fundamental personality types, and that everyone would fall into a specific box. That's good if you want to write a "what career is best for you" article for Cosmo, or for school kids. But it's bad science. Most personality traits are normally distributed, not categorial.
Most people are ambiverts, not introverts or extrovert. There's plenty of people who are heavily introverted, and plenty of people who are heavily extroverted, and it's useful to have a word for it, but most people aren't.
The other problem is, the traits it measures aren't important. Big 5 (Introversion, Openness to experience (i.e. culture / intelligence), Conscientiousness, Agreeableness, and Neuroticism) is better. It uses more interesting traits, and puts them on a scale (rather than using categories). It's not perfect (there's no real model, it's just common factors in personalities - psychologists often say it's overrated) but it's much better than MBTI.