I don't know how long ago this was asked, but I'll try to answer anyway. When you say "Il cavallo non è mio", you're saying that the horse is absolutely not yours and you may or may not own a horse. When you say "Il cavallo non è il mio", you're saying that the specific horse is not yours, but you own another horse. ...if I'm wrong on anything feel free to correct me.
It was asked 6 months ago.
The way it was explained to me (which I've explained on this page a few times 2 years ago) is as follows:
"La gatta è la mia" means "The CAT (and not something else) is mine."
"La gatta è mia" means "The cat is MINE (and not someone else's)."
But since there is no context in most of these sentences, both ways are equally accepted.
It is because it is written in a different order that they dont accept it. 'È non la mia zuppa' is your translation but theirs is different
The lessons are about vocabulary, grammar, and syntax. Meaning takes a backseat. Semantically, "The soup is not mine" and "It is not my soup" mean almost the same thing, but syntactically they are very different.
The soup is not mine. Here, "the soup" (a noun phrase) is the subject and the object of the verb is "mine", which is a possessive pronoun.
It is not my soup. Here, "it" (a pronoun) is the subject and the object of the verb is "my soup", which is a noun preceded by a possessive adjective.
Both are correct in Italian, but they have slightly different connotations.
When it's verb-article-possessive it means "this thing (and not the other thing) is someone's".
When it's verb-possessive it means "this thing belongs to this person (and not someone else)".
"La gatta è la mia" means "The cat (and not that cat) is mine."
"La gatta è mia" means "The cat is mine (and not his)."
In ordinary conversation, the two mean pretty much the same thing. But Duolingo's primary focus is to teach us vocabulary and grammar. So "It is not my soup" is marked wrong for "La zuppa non è la mia" for the same reason "the man and the woman" is marked wrong for "la donna e l'uomo". To the extent that it makes sense, Duolingo prefers the more strict translations over more fluid interpretations.
Both ways are grammatical, but they mean subtly different things.
"...è la mia" emphasizes "la zuppa" (as opposed to something else).
"...è mia" emphasizes "mia" (as opposed to belonging to someone else).
This only applies to the possessive pronoun, though. For the possessive adjective, you must always use the definite article (except with singular family members). So it would always be "la mia zuppa" and never "mia zuppa", for example. The exception would be that it's always "mio padre", for example, and never "il mio padre".