When will a Buddhist accept doing analysis? As the core goal of Buddhism is to cease sufferings, any task that not relevant to it will be unawarely ignored, and any task that hindering it will be strongly rejected. Analysis/intellect can either be irrelevant to the goal (as in, don't forget that the finger is not the moon), or an obstacle that Buddhists have spent all their life to fight (as in, it's the source of proliferation). However, in some cases where analysis is necessary to remove an attachment, automatically rejecting intellect means (1) the attachment is not removed, and (2) they don't think they have attachment at all. Or as someone puts it, they seem to have anti-thought bias, and I think anything they say would be thought-terminating clichés at that point.

How to fight this bias? How to make them realize that before you see the moon, as least you should have the finger? How to present them an analysis and they accept to read it as it is, rather than questioning anything irrelevant? 

Related:


intellectualism or anti-intellectualism and Buddhism  
I explain why I prefer discuss Buddhism intellectually but others don't seem to accept my point. Why is that?
How to ask other Buddhists doing analysis, rather than advising me to stop analyzing? 
How does philosophy not fall into the confirmation bias?
In the Hindu tradition they talk about four different yogas, or spiritual learning styles (the following adapted from the Vedanta Society, of whom I am fond):


Bhakti Yoga: the path of love and devotion. This path emphasizes practices such as prayer, chanting, and meditation on the loving presence in our lives.
Jnana Yoga: the path of knowledge. This path uses reason and discernment to discover the divine nature within by casting off all that is false, or unreal.
Karma Yoga: the path of selfless work. Those who follow this path do work as an offering and expect nothing personal in return, practicing detachment and equanimity.
Raja Yoga: the path of meditation. This path allows us to experience higher states of consciousness where we achieve a deeper understanding.


The Hindu tradition sees these as equally valid and non-exclusive, and while this can cause some confusion and consternation at times, it rarely leads to outright disputes.

The Buddhist path focuses on what the Hindus would call raja yoga. There are many examples of the other modes — e.g. the Bodhisattva vow, which is karma yoga; metta practices, which are bhakti; and studying the precepts and teachings, which is jnana — but since Buddhism has always been (to coin a term) 'anagnostic' (rising up out of innate knowledge), the other modes have always held a lesser place in its worldview. 

All of which is to say: you cannot expect everyone to follow your path, or to agree with you that it is correct, and if you wish to challenge a dominant paradigm you must first respect that paradigm and the people who practice it. 

I see you have a bee in your bonnet on this issue. You want to 'fight' a 'bias', and that attitude is itself problematic. The best way you can serve others is by understanding what they are trying to offer you. When you understand them, then you will be in a position to change their minds; not before.