Because "girl is eating fish" and even "girl is eating a/the fish" don't make sense in English - you need an indirect or direct article before the "girl" (either is fine, in this case), even though they don't exist in Polish. You don't need an article before "fish", however.
i've written "the girl eats a fish" and this is accepted. Sounds a little strange.)
"dziewczynka" is the diminutive form of "dziewczyna". You can think of "dziewczynka" as "little girl" if it helps.
Other than that, "dziewczyna" can also mean "girlfriend".
Well, still you have to write a correct English sentence, so you need an article.
I answered "A girl is eating fish" and it was incorrect without the "a" in front of fish.