You can be an introvert and still be arrogant. Having a dominant introverted function does not necessarily result in being timid and reserved. Having a dominant introverted judging function simply causes people to have a natural tendency to analyze and manifest their own internal preferences through their actions and behaviors. Strong introverted judgment causes one to analyze internally based on an internally categorized system, whether it's Ti or Fi. You are playing a game of semantics when you say that introverted functions will cause people to not "make claims" or be "demanding." People can be very strong in expressing their opinions even if their natural cognitive tendency is based upon an introverted function.
Also, Fi can be strong in those who use it as an auxiliary as well (ExFPs), and these guys are EXTROVERTS and according to your argument, this could result in being "demanding" and "making claims" (though I'm still going to disagree with your theory that "introverts" don't make claims or demands).
Pretentiousness is only more of an "extroverted" activity when that word is used to mean ostentatious. I already clarified my connotation though.Vanity or self-absorption would have worked better for Fi. Pretentiousness is more of an extroverted activity.