This child's father doesn't have to LIKE reptiles as pets, but he should respect and nurture his daughter's interests in them.
The pluses of owning reptiles:
1.) Many are small, require very little space for housing.
2.) Are hypoallergenic; many people with allergies to cats and dogs find reptiles non-offensive to their bodies.
3.) Are easier to care for.
4.) Eat less, and less often than mammals.
5.) Are easily handled... many leos, beardies and snakes are docile and suitable for occassional handling by children, under supervision, of course.
6.) Live longer than most gerbils, rats and mice. Many reptiles have the same life expectancy of cats or dogs, if not more.
It's a shame that this girl's father wants to push his own 'wants' in front of hers. Personally, I think a nice tortoise would fit into this situation. Many people who dislike reptiles in general often are open to turtles and tortoises. Tortoises also eat primarily vegetation, and easily cared for. A tortoise can become a lifelong friend if cared for properly.
Please update us and let us know what they decide on...
P.S. Didn't read above replies, so I apologize if I've repeated anything...