It's not a matter of which one is correct English; it's a matter of which one is the correct translation. "You and I" and "You and me" are both correct English, but they mean different things and are not interchangeable. "I" is a subject pronoun, and "me" is an object pronoun.
"You and I are going to the movies tonight!" - Correct
"You and me are going to the movies tonight!" - Incorrect
"Dad bought movie tickets for you and I!" - Incorrect
"Dad bought movie tickets for you and me!" - Correct
No. It is not always acceptable. You are simply wrong!
It is not correct English to say "you and me are going to the movies."
Nor is it correct, in English, to say, "They gave the book to you and I".
The job of DUO is to teach English as it is taught in English classes in the U.S.
No English teacher would teach as correct the examples I just gave.
Is the Duolingo German team ever going to fix this? "you and me" as translation of "du und ich" is abominably wrong, no matter how many times you hear it said by English speakers. I get that language is a living thing and changes over time and perhaps ten years from now it will be accepted as an expression, but today it isn't and you will find plenty of sources that it's grammatically wrong. The exercises containing this incorrect translation really need to be removed!
Ok, so in this question it asks to match words to translate "du und ich". However the only pronouns given by Duo as an option are "you" and "me", which is not a correct translation. "Ich" is nominative first person pronoun, which matches "I" in English. This type of error adds to the confusion around learning nominative/accusative/genitive/dative.
du is in the nominative case, mich is in the accusative case -- you can't combine those two together with und because they cannot perform the same function.
It would be like "him and I" or "he and me" -- "him and me" would be grammatical (e.g. "Mary saw him and me") and "he and I" would be grammatical (e.g. "He and I saw Mary"), but there's no occasion where "him and I" or "he and me" would fit.
Similarly, dich und mich could work and du und ich could work but never du und mich.
Both German and Norwegian are Germanic languages -- they both evolved from a common parent language we call Proto-Germanic. English is also related to both of those languages, though sound changes sometimes obscure the relationship a little -- the cognate of "du" is "thou" with a changed first consonant.
Norwegian belongs to the North Germanic family, a subset of the Germanic languages that also includes Danish and Swedish.
English and German belong to the West Germanic family, together with Dutch, Afrikaans, and others.
It depends on whom you ask.
Traditional grammar requires "you and I", yes.
But many people now most naturally say "you and me" -- the language is changing. To many people, saying "you and I" will sound old-fashioned, unnatural, and/or "talking like a book".
This course follows that change and uses "you and me", though it also allows "you and I".
If I were you I would just skip along out of this particular lesson and move on to another lesson which teaches proper English. (And German presumably - this is why we are here, oder?) ...or you could stay in this thread and be driven mad altogether. And you won’t learn any German at all.