The reason I say people should be allowed to bring pets to school is because some people will need service pets. I mean, if people can't bring pets either way, I think at least small animals (not dogs, cats, etc.) such as guinea pigs, hamsters, etc. should be allowed. You don't really meet anyone who is allergic to specific types of animals like these, and as long as it's a service pet, they're fully allowed whilst regular animals shouldn't be allowed as some kids can be allergic. As said, I'm the center of this debate but my opinion is still towards the yes side.
Kids shouldn't bring their pets to school for two main reasons:
1. There may be students who are afraid of dogs/cats/whatever the pets are. It is unfair to subject them to facing their fears for some sort of show-and-tell thing.
2. Kids may also have allergies to certain pets. Clearly, this is a safety hazard.