DD9 is a cautious yet fearless... she won't take any unnecessary risks, but if she's not aware of any risks, or feels that reasonable safety measures have been taken, she has no reservations. It has made for some interesting experiences. At younger ages she'd be OUTRAGED that she couldn't ride certain roller coasters, and seeing people be afraid of the ones she could ride was not something she could understand. And so, she wasn't very understanding. There were issues.

We've helped her by explaining that many times, fears are completely irrational, and the person has no control over their fear responses. We've given her a lot of examples of some crazier ones. My former colleague, for example, had a fear of sticks in food. If he was served a sandwich with a toothpick holding it together, he'd ask someone else to remove it.

In the OP's case, her child's reaction to the dog was just as irrational as the other children's response to the spider. Explaining that should definitely help with perspective and understanding.