Why do scientists classify a bat and a parrot in different groups?

Simply because the only thing they have in common is flight. Bats are mammals like I am. Parrots are birds descended from the dinosaurs. If you do not know what a mammal is remember this ,"mother mammals make milk", that is mammals give birth to live young, (not eggs) and mother mammals nurse the young, (they breast feed) like humans, cats, dogs, pigs, horses, sheep, whales, humans and all others that have breast, and breast feed the young. Bats have "breast" they feed the young. Parrots lay eggs, and do not have breast.