Usually, the conclusion is reached that YEC believers are anti-science.
I would say that might be true, but not in the way that it comes across.
The true root of this conflict has nothing to do with science, in and of itself. Instead the dispute arises from a mindset that knowledge has no neutrality.
Oh you mean they believe that the results are biased!
Yes and no. They believe the scientific results for evolution are biased, not because they think scientists simply are wishing evolution to be true and therefore massaging the data, though there is an undercurrent of that in YEC arguments. They believe the results are biased based on their theological beliefs about humanity and its ability to "know" things.
In a cosmology filled with angels and demons there is no middle ground.
Theistic evolutionists who are fighting to win over YEC believers are doomed to fail, not because of a lack of evidence, but because of the tenets of fundamentalist and evangelical Christianity. In a worldview that views humans as desperately wicked and blind to truth without an intervention from God, there is no motivation to trust what scientists say, especially scientists who don't believe in any sort of God, or any form of Christianity.
It simply isn't possible, with this mindset, to think that any person could objectively discover the truth about the universe, creation, and humanity without special revelation from God.
Certain Scriptures don't really help us out here, either.
2 Corinthians 11:14
14And no wonder, for Satan himself masquerades as an angel of light.
1 Corinthians 1:20-21
20Where is the wise man? Where is the scholar? Where is the philosopher of this age? Has not God made foolish the wisdom of the world? 21For since in the wisdom of God the world through its wisdom did not know him, God was pleased through the foolishness of what was preached to save those who believe.
1 Corinthians 1:25-27
25For the foolishness of God is wiser than man's wisdom, and the weakness of God is stronger than man's strength. 26Brothers, think of what you were when you were called. Not many of you were wise by human standards; not many were influential; not many were of noble birth. 27But God chose the foolish things of the world to shame the wise; God chose the weak things of the world to shame the strong.
1 Corinthians 3:18-20 18
Do not deceive yourselves. If any one of you thinks he is wise by the standards of this age, he should become a "fool" so that he may become wise. 19For the wisdom of this world is foolishness in God's sight. As it is written: "He catches the wise in their craftiness"; 20and again, "The Lord knows that the thoughts of the wise are futile."
There are certainly times when evil might appear good. There are times when a wise choice looks foolish on the surface. It is true that knowledge does not necessarily lead to good choices.
These Scriptures are not "untrue" in what they communicate, but they certainly help feed the YEC conviction that believing something that makes no sense is further proof that they are on the right track. Any argument about a scientific theory which would remake the foundations of this version of Christianity will fall on deaf ears, because those ears have been conditioned to hear,"Just because smart people say it's true doesn't mean it is."
Those smart people might have been taken in by what appears to be an "angel of light" but is really just a harbinger of evil and destruction.
There is no way to overcome this view of humanity without completely reformulating opinions on whether man is a neutral being, and whether knowledge can be objectively obtained.
That may seem like a trivial thing, but it isn't. It permeates layer upon layer of thousands of years of theology.
Theology is like a giant game of Jenga; some pieces can be removed with little consequence to the overall structure, other pieces cause inescapable collapses of the entire tower when they are even slightly shifted.
This is what YEC advocates sense and what fuels their protection of their particular tower.
They see the wobbliness and are desperately holding their breath waiting for the tower to stop swaying and be still once more.