I have come to realize that there are many things that are specific in Italian as oppose to English. Your answer "the animal eats its own meal" in English could be interpreted as "the animal eats its own food" as well since when you eat a meal, you're eating food. This is not the case though because duolingo is asking for a specific term: food. So to answer your specific question, because meal in Italian is pasto, whereas food is cibo.
Hope this helps!
Without the article, "l'animale mangia proprio cibo", it would mean really/precisely/indeed, although it would be a strange sentence, marveling at eating food of all things. As adverb, those are the meanings of proprio, but as adjective and pronoun it generally means own (see http://www.collinsdictionary.com/dictionary/italian-english/proprio for all meanings).