This topic confuses me. If you're having tests on how many letters are in the alphabet, you must be pretty young. If you're teaching kids on the alphabet you're not going to get into some random philosophical discussion on the difference between capital and lowercase letters and whether they constitute wholly new letters.
This sounds like a question and discussion used in a philosophy class to try challenge a concept.
I think you're more right than the teacher, however in proper grammar, you wouldn't use the capital and lowercase forms interchangeably. So the teacher has a small point, but I wouldn't consider lowercase and capital forms of a letter different letters.