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.
In the belief that I correctly understand your question, and keeping in mind that my knowledge of Russian is rather limited, Friend Mantpaa, here’s my effort to answer your query. Please note that I had difficulty with this same issue recently, until it was explained to me by several folk more fluent in the tongue than me. The word in question means “man” and is, therefore, masculine in substance. However, the word in Russian is (strangely enough) feminine in form and is to be declined as a feminine noun. And if you think that is more than a bit odd, consider this. Although such masculine (in substance) nouns are declined as feminine nouns, the adjectives which modify such masculine (in substance, not form) nouns, are declined with masculine endings. That is, in my not-so-humble opinion, one very illogical crazy-making rule. If, perchance, I have misunderstood your question or have incorrectly stated the pertinent Russian rule of grammar, let’s hope that a native speaker or one more fluent will come to our rescue.
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