Why is it significant that Edward's special skill doesn't work with Bella?

It allows Edward to actually experience something new for a change. His life had been full of monotony until Bella came around. He got to know what it feels like to wonder about someone again, like a normal human, and even a different vampire. He's the only one with his power, so he had no one to relate to, until he met Bella.

It gave Edward the prompting he needed to take interest in Bella, because she was different and it frustrated him.