I consider INTJs my best intellectual rivals / greatest allies depending on the subject(s) being discussed and where our biases fall.
INTJs are much more refined in their delivery of the facts than I am and typically desire closure to some topic or issue. Quite the opposite I prefer to leave a topic open ended to some degree and the facts truly have to be overwhelming in order for me to close the loop. Conversely they (INTJs) can struggle when handling a theory especially just being able to freely turn it around in their heads and analyze a perspective solely on its logical implications. For the INTJ a good argument doesn't mean anything if it can't be applicable in some actual working system.
I think in my ENTP view I see INTJs as slightly pompous and its clear they desire status and recognition (and maybe even accolades) for their intellectual prowess. They can be haughty and stubborn but , to their credit , can usually back up their ego. INTJs I've met usually have a reverence and respect for those they deem intellectually equal or even superior and believe it's not exactly wrong to categorize people in an intellectual hierarchy.
For example : Someone else challenges something the INTJ considers to be valid with a cleaver argument. The INTJ may believe it to be true because of intellectual authority has deemed it so and may minimize the veracity of an argument just because the person making it doesn't have some kind of recognized intellectual status.
ENTPs don't really care about intellectual status or even recognition. ENTPs are perfectly fine being 'common' among the masses with everyone else and think of our intellect as something usually fun and some toy/hobby to be played with. We see
everything as an intellectual playground rather than some academic pulpit to effect holistic thought on a grand scale. INTJs are formal with their intellect while ENTPs are tongue and cheek and casual with ours.
I think this annoys INTJs about ENTPs since they recognize an equal or similar intellect but believe ENTPs waste our 'talents' with our frivolous approach.
On the flip side there is a unique synergy here that can't be overstated. My best 'sparring partners' have been INTJs on virtually all matters. It's fun and at the end of the day nobody's feelings are hurt.
