Yes, I would care very much if my child was missing and the police arrested me. Talk about what is a natural human response! I would be distressed beyond words that LE was focused on the wrong person, and possibly overlooking clues/evidence that could mean the difference between life or death for my missing child.
I try not to imagine the actual horror of ANY of the criminal cases I read about or have followed, especially those involving missing/violated/murdered children, which for the most part I avoid altogether- too painful.
But yes, as a mother who would literally & willingly die for my son if it came to that, I can readily accept that I'd almost certainly feel the agony you describe if...
Maybe we are simply talking past one another, though? I didn't say I would stop talking to LE, nor that I'd stop cooperating. It seems a false (and dangerous) choice to assert that one can either cooperate with LE OR one can protect oneself.
One can do both. One says to LE- I need desperately to help you find my child, but since it looks like you are turning your focus on me, I also need to protect myself, for my sake,and for my child's sake, because your focus on me might be wasting irreplaceable time . Lawyer. Now. Please.