INTJs believe they are right, unless they don't believe they are right, in which case they won't comment. This makes people think they're very arrogant.
So often I've made errors of interpretation. People get into arguments with INTJs and end up with "They told me that their argument was the same as my argument the whole time, therefore they won! What an asshole!" I cannot say how many times this has happened to me, only I see the source. An INTJ may phrase something in a specific way because they want it to be interpreted a certain way, while another person will explain that they are wrong while arguing the same thing. Such as, well, overly-simplified, "90% of people don't die in car crashes" "No, you're wrong! 10% of people DO die in car crashes!" Well, the complexity of language makes it much, much harder to decode but it's more or less the same thing. Because of emotional stakes in these sorts of arguments the INTJ may smugly point out that they've been arguing the same thing the whole time and the other person will get mad.
INTJs get upset when somebody shrugs off their reasoning without proving that they understand it. To convince an INTJ that they're wrong you have to prove it up, down, and sideways -- and admittedly, this would be frustrating for most people.