Strength never comes by showing understanding for the weakness. You overcome fear by facing the tiger with your fear and discovering that you can walk away alive. In time you laugh at the tiger, for it was only paper. But if your child flees from the tiger, and you call it fear and then offer sympathy or protection, you legitimize the child's fear and the paper tiger gets bigger and more threatening every day. If you treat the paper tiger with indifference, the child will feel the same.
Wild animals learn what to be afraid of and what to tolerate by watching their parents.
You will make the child into the image of your own responses.