Types vs. Traits: Why Personality Types Exist

I don't often get triggered by people being wrong on the internet (https://xkcd.com/386/). However, when I read "MBTI is astrology for nerds" by well-respected academics on Twitter, THAT triggers me. And it happens surprisingly often.

Thus, I decided to write a logical, scientific proof for the existence of personality types (as well as calling out the problems with the Big Five and why Big Five followers are the true cult).