We've all ran into those people in the course of our socionics adventures who are resistant to being typed. They don't want to be forced into any box and no matter how much explaining you do they still claim that they exist outside the theory entirely, or rather it's easy to tell that that's what they aim for.
In my case it's alphas. More specifically the alpha introverts, even more specifically LII's.
I'd be really interested to see if there is some correlation between the user's type and the group that is most resistant to their typings.