So I'm in this argument with my friend...?

You are correct. You wouldn't say "a hour" or "a M". Hour does begin with a consonant, but it has a vowel sound, so does the letter M. That applies to any word that begins with a consonant but has the sound of a vowel. A slight exception might be the word, "historical", as in "It was an historical event". But it would also be correct if you said, "a historical event." There is nothing quite as confusing as the English language.