Final answer:
The teacher should caution against bringing the bat inside because bats can carry rabies and other diseases like white-nose syndrome, which is harmful both to humans and to endangered bat populations.
Step-by-step explanation:
The teacher should deny the request to bring the bat inside and caution everyone to stay away from the bat. Bats can be carriers of diseases, such as rabies, and should not be handled without proper training and equipment. One particular disease affecting bats is white-nose syndrome, a fungal infection that has severely impacted bat populations, including some endangered species. Handling bats not only poses a risk to human health but also to the fragile state of bat populations.