It could be because we don't really ever talk about people like that in English.
We may use a/an like that when referring to inanimate objects, as in "a house has a roof" but even then, "houses have roofs" sounds better.
Unless you're Jaq'qen Hagaar from Game of Thrones: "A man is learning Russian"
we don't really ever talk about people like that
in Russian too :)
The sentence is quite unnatural.
The creators of the course try to illustrate the idea of the absence of articles in Russian, using rather limited lexical material and sentences which are sometimes only relevant in a grammar textbook as a scheme, but not in real speech.
I have not resolved this issue, but from what I can tell, although мужчина is a masculine noun (мой мужчина is correct, not моя мужчина), it appears to be declined according to the rules for feminine nouns because it has a feminine noun ending in nominative case. Bluntly, мужчины is the genitive ending for a singular noun according to the feminine table of declensions. I can't recall the word, but there is another instance of this I have worked on.
Strange as it may seem, Friend Jeffrey855877, it seems that masculine Russian nouns ending in “а” or “я”, though masculine, are declined as though they were feminine. But stranger yet, adjectives and pronouns describing those nouns are declined as masculine. In my not-so-humble opinion, that’s just more circumstantial evidence that the language was concocted by sadists.
It's weird for English and Spanish speakers, but grammatically сестра is the subject :P The sentence is something like "By me(genitive) is (a) sister", so a sister is by me, and thus is the subject. Something similar happens with sentences like "I like vodka". Vodka is the subject in those sentences, because the Russian sentence is more or less something like "Vodka is (something I like)". But amazingly that one also happens in Spanish, just like "double negation", "what" and "that" being the same word, and many other similarities.
It's just a question of reordering the words to put them into a more familiar frame of reference: The Russian literally is "By the man exists/is/belongs a sister". If you put that into usual English word-order, it becomes: "A sister is by the man".
In that format, "sister" is the subject thus is in nominative case and "man" is the object of the position у, placing it in the genitive case. (Note: not all objects of prepositions are in genitive case.)
Idiom. It's just the way Russian expresses the idea: "the [noun1] has a [noun2]"
The Russian literally means "By the man is/belongs a sister"
y is a preposition and it means "by/from". The reason мужчины is in genitive case is because it is the object of the preposition y
Russian has only a limited number of word endings but more declensions so they end up using some endings in multiple ways. As such, most feminine and neuter words will use the same ending for genitive singular and nominative plural. This isn't true for most masculine words, where the two forms are different. It's not a bad thing that endings get used in multiple situations, ultimately it's better if there are less things to learn.
I wish Duolingo explained grammar. To my understanding thus far, it appears that the Russian language does not have articles (e.g. the, a, an in English, un, unos, las, los etc in Spanish)
мужчины = man
есть = has
сестра = sister
мужчины есть сестра = man has sister
Which, cleaned up to sound like a proper English sentence becomes "the man has a sister"
У мужчины есть сестра
So, what is the У doing at the front of the sentence?
You are correct that Russian has no articles. Now Russian does have a word that means "to have" (иметь) but usually they will do things a little differently. "у" means "by" and есть means "there is". Instead of writing "The man has a sister" they will transliterate "By the man there is a sister" => У мужины есть сестра.