It's not weird. Most cartoon characters are animals. Most animals' eyes are reflective and seem to glow in the dark.
Still, reflective to light is not the same as glow in the dark. Someone very weird must have come up with that concept :s
It doesn't take much light. The light of the moon or campfire is enough. I've spent plenty of time in the wilderness and when you look into a forested area it's quite dark and foreboding. If you happen to spot a creature (usually a raccoon), it's often only their eyes glowing in the pitch black darkness that you see and not their body.
Cartoons tend to exaggerate, too. Hence, they also make people's eyes glow the same way.