INTJs seem a bit odd to others. It is as if they have very little to say most of the time, but when they speak they “know” they are right. For most people this seems like INTJs spend a lot of time being mysterious then come across as arrogant when they choose to speak.
What is actually happening is that INTJs build these really complicated, fact stacked on fact, knowledge models in their heads and, unlike the vast majority of people, don’t talk about stuff they don’t know much about. When they do talk it is because their fact-model is relevant and they “know” the answer – it all stacks up.
INTJs are not mysterious, they are just a lot more sensible than most people – and because most people don’t want to be sensible too they like to see INTJs as mysterious – this allows them to happily keep making stuff up and ignoring evidence etc.
Note: as an ENTP I make stuff up lots of the time, but I am well aware I am being lazy and ignorant when I do – I don’t argue with INTJs unless I have very strong evidence 😉