The only problem with this is that the civilian command authority has the power to initiate a court martial, which recognizes the civilian link in the chain of command. It would stand to reason that this should be able to go both ways, with no limitation on the ability of service member to question all levels of his or her chain of command. Plus, doing so aligns with the oath to support and defend the Constitution.
Don't ever conflate reason with law. They are entirely separate.
There are ways to legally seek redress through the rising levels of command with respect to issues or policies you believe to be incorrect. Refusing orders isn't one of those way.