It is not a question of incredulity.
You appear to think you have a basis for your claim - you're wrong, but let's work on the assumption you think you have an argument.
It is simply a total impossibility - derived from the simple logic that any consciously confirmed logical deduction requires guidance and control of the thought processes needed to reach and confirm such conclusions.
What 'logic' is that? You don't appear to be deducing that from anything, you're just rephrasing your a priori assumption as a conclusion. Why must you have some 'conscious control' in order to come to logical conclusions? Computers can come to logical conclusions, and there's no evidence they have free will or consciousness.
You imagine that such guidance and control can simply drop out from the uncontrollable material reactions occurring in a material brain.
Nobody is suggesting any 'simplicity' about this - the human brain is one of the most, if not the most, complicated structures known to science. We have barely begun to scrape the surface of the depths of feedback mechanisms and interconnections involved in the brain - to assert definitively that there are demonstrable human behaviours that are beyond the possibilities of the human brain is to suggest that you don't understand the complexity of the human brain.
Any reasoning or evidence you come up with must be a consequence of your ability to consciously compose and confirm such reasoning.
You are presuming your conclusion as an argument for your conclusion, here - that's circular reasoning.
Why can't you understand this simple logic?
You haven't shown any logic. You've reasserted your conclusion, and called it a logical conclusion. Your entire argument is a single statement of 'that's impossible' without any justification whatsoever.
Are you afraid of the consequences of admitting that you do have the conscious freedom needed perform such reasoning?
Which would be what, exactly? Even if we assume that 'free will', despite being self contradictory, were a thing, what are the consequences of accepting it?
Where you go wrong is not in the reasoning itself - it is perfectly sound reasoning which you use to conclude that our conscious freedom is a logical impossibility, but it is only a logical impossibility from the materialistic premise.
If you're wanting to suggest something beyond a 'materialist premise', you need to explain what mechanism you're going to use to validate your proposals. You're quite happy to venture unarmed into the materialist realm with your assertion that consciousness can't be a result of purely material reactions, you aren't relying on any demonstration of anything non-material for your argument. You are concluding that there must be something non-material, as a result of discounting - without basis - the material explanation. You have no argument, you have an assertion, and a claim of magic as a result of that assertion.
Do not be afraid - you are made in God's image.
Only if God's an atheist sceptic...
O.