That seems unfair and stubborn though, and I don't think INFJs are like that (but that's the picture I get from how you've explained here).
Unfortunately, for the most part, we are like that. All types have their strengths and weaknesses, which are often the same functions. INTPs for example have an amazing ability to brainstorm, but with it comes a need to explore all possibilities, to such an extent that can be misconstrued as their own opinions.
If one of those beliefs in your web are proven wrong, isn't it your responsibility to reevaluate the parts that the belief has an effect on?
No. Logical proof is not always proof, especially to a Feeling dominant personality. Over and over in history, people have stuck to their guns and been ultimately proven right when repeatedly 'proven' wrong.
A classic example is a sales debate. If you don't feel that you want something, but a salesperson 'proves' your objections to the sale wrong, are you obligated to make the purchase? No. The reason for this is simple. Proof is rarely all encompassing, and almost always subjective and situational. Most importantly, it doesn't change the way you feel. If it does, you've got little self integrity.
To make a more corruent example, I've proven repreatedly through logic that a human being is incapable of determining the existence or lack of existence of God. You seem to feel that this is not the case, and therefore won't reevaluate your stance to include the possibility.
And, don't take it the wrong way, but Ni is just as good at building connections and a system off of false beliefs too. If your starting point is false, and you make connections to that...then the reasoning from your starting point to other beliefs is likely to be false.
I agree with Satya. Ni goes from no starting point to a single end point. Ne often goes from one starting point to no end point. Ne is an explosion of possibilities, radiating out from a single source. Ni is an implosion of all sources compressing into a single possibility. Whether or not that is the correct possibility, it is the one we
feel is correct. Or in the case of INTJs, think is correct.
As an INFJ, I
feel that the existence of God cannot be proven or disproven. My Ni brought me to the notion, my Fe allowed me to feel what my Ni has developed to be the case, and my Ti has validated my Fe to an extent that my Fe is now bolstered. Throw in the fact that my Se has shown me evidence to support this state of absolute inconclusiveness, and even my Ti has reinforcement. When all four of an INFJs functions agree, it is nearly impossible to penetrate our stances. No amount of logic is going to press any further than our Ti. From there, you'd have to disarm our Fe, and then Ni, in order to get us to budge. That cannot be done with 'proof' alone. We need more than that.