Adam is afraid of everything, it seems. Open spaces, closed spaces. Dogs, teenage boys. Being alone, being followed. But the important question isn't what does someone fear but why do they fear it? We learn throughout I Am the Cheese that Adam has reason to fear everything around him: since his family is in hiding, they never know whom or what to trust. Every knock on the door is frightening. Sounds like a horror movie, right?
For Adam, the unknown is more frightening than the known.
If Amy were in Adam's situation, she wouldn't be as afraid.