We're just so far off from the norm that we don't seem to be understood by anyone but one of our own (I'm grateful for the INTJ forum).

There's a stereotype that somehow implies INTJ females are not 'womanly' and there's somehow something wrong with speaking, thinking and acting like a 'man', which, might I mention is another stereotype (just like it's wrong generally for boys to be interested in dolls instead of war games). There's been much fuss about how INTJ's are cold. I would like to point out that we're not (or at least, I'm not). I don't like to communicate my emotions, and hardly anybody but myself know what I'm thinking most of the time. Whenever I was hugged, I tend to flinch and
nicely explain why I'm not comfortable with being hugged. That didn't really distant me from my emotionally expressive friends and they understood. Not many people know us personally. I myself have a wide circle of close friends, but among them, I can only vouch for 2 of them to really know me (and in any case, I only truly like these two). Even then, I have more than 50% of myself kept from my closest of confidants. They're the people I 'click' with and I find that I can admire, whether it be their intellect, character or achievements who share a similar depth of thought with me (and those who realize that there is more to the world than fashion, dating and 'having fun').
Even though I'm good at it, honestly, I hate acting. With most of my friends, whenever I start on a subject that really interests me (science, politics, philosophy etc), they find the quickest way out of it and change the subject to gossip, flirting and complaining about how stupid people are (they really have no rights to do that) I have to act silly and immature around them or I'd be considered 'no fun at all'.
Some of us do not think that most people are competent because they don't make 'sense' or that they are not decisive/focused enough on a task. (I'm generalizing, but only from my observation) We admire the purest of logic and the courage to admit that one's wrong. That is a discipline most INTJ's follow and some of them expect the same of others. That may come off as arrogance to the general populous, and I really don't blame them.
Might I mention that most INTJ's prefer to handle things and see the world through a detached point of view? That might anger most F's and some other T's.