I've known "umieć" as being a verb used for 'knowing how' to do something. Would it not be better to have it as "to know how to" as opposed to "to be able to", as currently it's a bit too close to "móc" to notice the difference. (Please tell me otherwise if I'm mistaken.)
The translation now appears to be "can" rather than "able to". So, referring to your "know how to" point, when we say something like "I can swim", nine times out of ten we are talking about general ability: i.e. that we know how to do something, and I think it's rather more common to use "can" than "know how to" in this context.
In some languages this use of "can" is translated wih a verb for know, e.g. "Je sais nager" (fr). Similarly the standard Polish translation of "can" in this meaning apears to be with "umieć". From Collins Słownik:
"I can swim - umiem pływać"
So for me, while "Why don't you know how to cook?" is fine, "Why can't you cook?" is possibly more natural here, and that more importantly, Duo are right to show this relationship between "can" and "umieć".
(Corrected - thanks to 880201)
I don't know what dictionary you're referring to but this is from the PWN/Oxford Wielki Słownik:
"nie umiem tańczyć/pływać - I can't dance /swim"
When talking of ability, "be able to" has exactly the same meaning as "can", and we can often use either. The only difference is that when there's a choice "able to" sounds a bit formal so we usually prefer "can/could". And that sometimes "can/could" is not possible and we can only use "be able to":
"He can (is able to) to do it tomorrow"
"He should be able to do it tomorrow"
"Why can't you cook?" (Duo's Android app answer), is fine here, as would be "Why don't you know how to cook?"
Yes, I fell into that trap too and became confused with ;able
Yes, I too became confused with the English 'can' and 'able'. I know that umieć is to know how. So when I wrote 'Why are you unable to cook' Duo found it unacceptable. English words are so slippery in their meanings!