"today is not Monday but Wednesday" sounds horribly unnatural to me (native English). I would say "today is not Monday, it's Wednesday" much more often. It's crazy to mark that as incorrect - there's no difference in meaning. Just because the Czech expression uses "ale", doesn't mean you have to shoehorn in the equivalent word in English.
The "but".... Is wrong throughout this course. English speakers would never ever use in a phrase like this. Today isnt monday, ITS Wednesday. ,"Ale" is literally "but" but since the rest of the course is not translated literally word for word, neither should this. I refer to žena which is always taken as wife, and woman is not accepted.
While I would disagree that native English speakers would never say "Today is not Monday but Wednesday," it IS a bit on the formal side. Use of "Today isn't" or "Today's not" is probably more common. (My answer, which used "today isn't" was accepted.) But I don't think there's anything wrong with the translation given.
----- UPDATE ----- Seeing this again, I realized that my comment did not address the "but" construction used in the main translation. While I'd agree that most (US) native speakers may not use "but Wednesday," there are definitely many who would and I don't feel it's unnatural at all. "But rather" may be a more BE formulation.
I have to check your claim first (not ... but rather ... is certainly correct, but I must doublecheck without rather)., but your comparisan with "žena" is strange. We certainly accept both wife and woman, but of course each of them only when they are the appropriate translation.
Sentence "zvláštní žena" in skill Feminine in Tree 1 does allow both woman and wife (and also lady) as an accepted answer.
"but rather Wednesday" isnt correct either. Maybe "but rather its..." then you may as well just say ,,its Wednesday". Zena is never accepted as woman when its tvoje zena "your woman" or muj muz is only accepted as my husband. Which I accept, but in English you can say your woman without it being your wife.
IMO, most native English speakers, at least in the US, would probably most often say something like, "Today isn't Monday, it's Wednesday."
But I (native AmE) am mystified by the comments saying that "... but Wednesday" is weird, wrong, or both. And I do think that "... but Wednesday" should remain the main translation, as there is nothing at all wrong with it in English and it's closest to the Czech sentence. Also accepting the more common "...it's Wednesday," however, makes sense to me.