I'm not a cognitive science expert, but I happen to have some experience in change management / trying to convince people. There are in fact a lot of logical reasons for refusing logical and rational arguments.
Suppose someone tries to share an idea with you.
I will pass on the very obvious problems of "not befitting my interest" / "triggering culpability".
A VERY common problem is the fallacy that, "If I am wrong, then my opponent is right." If you hate your opponent (or whatever maybe impolite person is trying to tell you to change your ideas, e.g. your "bad way of living", or arrogantly seeing you as a miseducated inferior), then you'd rather die than accept that idea, which would $\rightarrow$ (fallacy) prove him right and thus $\rightarrow$ (fallacy) superior to you.
Another common problem (colleagues!) is, "I must show I'm the most intelligent." If someone tries to challenge one of your ideas, then it $\rightarrow$ (fallacy) makes him more intelligent than you, since $\rightarrow$ (fallacy) you were wrong. You will then try to find whatever counter-argument you can to prove him wrong, (fallacy) $\rightarrow$ thus reasserting yourself as more intelligent.
Another common but more subtle problem is that we all unconsiously build a representation of the world so that we can think on how to adapt to it (evolution). And of course we stabilize this representation when it fits correctly $=$ when we are in no immediate danger and also when we are in a comfortable position ;) Example: "The society rules are that people who adhere to the dominant opinion are more likely to succeed" (adaptation to environment) $+$ "People who don't share this dominant opinion are fascists/integrists/extremists, etc., who are a minority anyway" (rationalization of why I adhere to it, advantageous position). Now suppose that an idea challenges your representation of the world. Then it implies $\rightarrow$ that you are no longer in a superior position, and $\rightarrow$ that the rules of the world may not be what you thought, and that $\rightarrow$ you may be bad at understanding the world, thus in a weak position for planning corrective actions ($=$ adapting). Such a calling into question is incredibly painful! To evolve from this situation, one needs to experience full grief (as in "Five Stages of Grief").
I speak from experience. I once had the mindset, "Rules of the world are following religion X" $+$ "Those who don't follow religion X are pagans/heretics/whatever bad people" (but it's the same even outside religion). The challenge was when I realized after an event that $1)$ I was not that good, and $2)$ "pagans/heretics" were actually better than me on this subject. This triggered a very painful 5-stage grief process over more than 6 months where I suffered a lot before re-establishing a new, more correct vision of the world fitting those new pieces. I still needed a few years to fully unwrap things. From my experience, it seems I was lucky to be able to do that since it's not a given (cf. all possible failures of the 5-stages). And seeing backward, it was not the fault of religion X at all. I had built this simple and a bad representation myself to avoid facing some unpleasant truths.
Another common problem is the incorrect mixing of opinions and culture, which fallaciously leads to: idea challenged $\rightarrow$ (fallacy) culture challenged $\rightarrow$ (fallacy) our identity is challenged $\rightarrow$ (fallacy) our ancestor's work and worth challenged. Who would want that?
What you should understand is that the mind needs some security and self-confidence. All the mechanisms I exposed are mostly subconscious and argument rejection results mostly from an auto-defense of the mind, though we still have partial control over it. (I'm sure you have examples of people who honestly face the truth and others who never want to face it.)
If you encounter people that have realized all those points, discussion is easy even if you are not polite or your ideas are not well refined. They will look at the good points, accept the ideas and even help you refine your ideas. This is how everyone should be!
For other people, I've found that challenging ideas is better done when:
- you are polite and non-threatening
- you first outline the strength and qualities of the people you speak to their culture $+$ their ancestors
- you clearly separate the challenged ideas from culture and show similar idea change by good/respected people in their own culture
- as much as possible you make the new idea look like it comes from themselves.
Oh, and one last thing: humility. Everyone trying to spread an idea obviously thinks of it as "logical and rational", so if it's not accepted $\rightarrow$ (wrong!) it means that people are not rational $\rightarrow$ (wrong!) people need to be reeducated $\rightarrow$ (wrong!) there are some horrible opponents who fight my ideas, I must suppress them. Such thoughts led and are still leading to atrocities. Maybe it's just you who are wrong, illogical and irrational ;)