"I have the fish."
You mean "ryby" and "rybę"?
"ryby" - is plural (Nominative and Accusative) form of "ryba" (and singular Genetive as well). "rybę" is singular Accusative form of "ryba".
"I have the fish" means "Mam rybę". "Mam ryby" should be translated as "I have the fishes".
If Duo marks you wrong for "Mam rybę", please report it.
I can think of using Polish plural here only if the English sentence was "I have fish" - without the "the". A fish seller could say something like that thinking of more than one fish that he has for sale.
Yeach, after rethinking it I admit that you are right. The plural form of "fish" (fish/fishes) depends on the context that wasn't given here.
So "mam ryby" can be translated either as "I have the fish" or as "I have the fishes".
However the question asked by Puechgaubil concerned the reverse translation in which - I guess - only "mam ryby" was accepted as the correct answer.
'Fish' is both singular and plural in English, so 'mam rybę' and 'mam ryby' both translates to 'I have the fish'. English 'fishes' is used when talking about species of fish. If you went to a marine museum and said you saw two fish, that would mean you saw two individual fish. But if you said you saw two fishes, that'd mean you saw a few individual fish of two different fish species.
Polish 'ryba' and 'ryby' doesn't do that distinction. Both refer to individual fish, but plural talks about more than one. The species (gatunek) matter is a different kettle of fish whatsoever. ;)