In English we say "You and I take off" when talking about leaving too.
"You and me" is only correct when "we" are the direct/indirect object of the sentence; when "we" are the subject, it has to be "you and I".
"You and I punched a gorilla. The gorilla punched you and me back."
If you take out the word "you", you get:
"I punched a gorilla. The gorilla punched me back."
Removing "you" from your sentence makes it "Me am leaving" instead of "I am leaving".
That being said, "You and me are..." is just about the most common grammatical error I can think of, and doesn't sound the least bit strange when I hear it in day to day speech.
The same rules apply to danish, distinguishing between du og jeg and dig og mig.
Kim og jeg henter is til min søster og mig. (Kim and I get ice creams for my sister and me)
It should, but that is older English (Swedish and Danish translated literally follow more the kind of English I'm used to hearing from Jane Austen movies than current English). It's correct, but you don't usually hear "I will take my leave of you" anymore.
I was wondering if Danish pronunciation is so difficult or just Duo audio is broken. Or maybe my ears are not trained to Danish sounds... :D