Translation:Birds fly in that direction, but we do not.
A madarak szabadok, mi pedig rabok vagyunk abban a börtönben, amelyet életnek nevezünk.
There is a mistake. It should be: A madarak instead of Madarak (because of the English The birds). So I am a bit disappointed it did not count my correct sentence as correct ...
"Madarak arra repülnek" is just plain unnatural without an article.
"Madarak repülnek arra" is good, but it emphasises "madarak", therefore it doesn't fit with the second clause, which requires either "arra" or "repülnek" to be emphasised.
I think the main reason the article is necessary here is that the sentence makes a contrast between "we" and the birds, so the birds have to be better defined/highlighted.
Yes I agree. We need the definite article in English for this to make sense.
Use 'hanem' as a conjuction when you compare similar sentence elements. "This bed is not blue, it is red." "Ez az ágy nem kék, hanem piros."