When your child is sick or scared, you take her in your arms, pat her head and say, "Don't worry. You'll feel better." or "Don't worry, everything will turn out fine." And often that is indeed the case.
But those words of comfort are often actually destructive, especially when spoken to an an adult. When you say, with a cheery upbeat voice, "Oh, don't worry, you'll be fine," you deny the validity of the person's feelings, and indeed imply (though you may not realize it) that he or she is misguided or stupid.
Here's what people in distress might prefer to hear:
"I respect your distress. I respect how you are feeling."
"I hope things will go well. I want to offer you my positive thoughts (and prayers, if that is meaningful to you)."
Of course, we all wish the best for those in distress, but we must be careful that our words don't leave the person feeling invalidated and even more alone and scared.