An is the singular definite article, "the". The module is 100% consistent in using an in the Irish sentence when the English sentence has a singular definite article, and not using an when the English sentence has an indefinite article. There is a mix of sentences with either definite articles or indefinite articles precisely to make this point.
Duolingo is pretty fussy about writing exactly in the same order you see and hear. Otherwise, if they say or write "boy and girl" and you translate it as "girl and boy", the computer can't tell that you really know the words. All it's programmed for is that you did not say "boy" when you should have, and you did not say "girl" when you should have.
So, as far as the program goes, you've got to write it the way Duo says. As far as speaking on your own, do what you want.
Dou, heres a suggestion. This is difficuktbsnd the forms can seem "unnatural" to a native English speaker like me (no qualitative judgement here). Inbyour French course you have an excellent system where you have litle "key guides" to what is going on in that chapter.
How about being helpful and doing that for ALL the languages youbteach, please?