The lack of facts were from me being lazy and assuming that you had the same data that drove the assumptions I made. Plus the dyslexic thing sometimes means that without thorough examination of my writing I miss mistakes since looking at similar patterns can make me feel disorientated.
Introverted intuition is irrational claim
Read Jung description of introverted intuition several paragraphs below and you find out why he describes it as the most irrational of all the perceptions. Both sensing and intuition are stated as being irrational but intuition is said to be more so than sensory, and from that he also states that when the perception function is introverted (Ni/Si), its less concerned with "objective" reality than its extroverted counterparts.
Classics in the History of Psychology -- Jung (1921/1923) Chapter 10
The idea of the INTJs having the highest sub minority of atheist is an assumption based on that sample you stated. I just gave you my reason that my assumption is based upon, my aim is in not being "right" but gaining further understanding (plus empathy doesn't mean agreeing its just knowledge). And again with the Ni and "irreligiosity" correlation assumption was based on analyzing some of the properties the NiTe relationship which makes us quite independent (getting along with others on the interpersonal realm is stated as an achilles heel for us since we are fiercely independent (without addressing this we have difficulty dealing with the other types (INTJ Personal Growth))). And that's were the perceived "arrogance" claim was based on and its a common state regardless of whether the INTJ is religious or not. Plus from, the religious INTJ debate forums I learnt that the reason to why an INTJ can accept religion tends to be vastly different in comparison to other types since from what I heard, the religion is supposed to meet the given INTJs idiosyncratic system and not the other way round.
Why the rage?
Why the rage? Why are you taking this to heart? If you are drawn to get personal over this (any argument) then you'll defeat any objectivity in the argument and simply get centered around "winning". Third order and Second order thinking are important frameworks in assisting objective thinking since awareness of our biases is gained (plus the why factor). If the line before feels condescending, its actually not meant to be (but that's the limitation of lacking the power of speech tone of voice...). To be honest, I tend to expect people to look at arguments objectively and not get wrapped around any feelings accidentally evoked.