I apologize for asking the same questions, but why "κοτόπουλο"?
I can understand "η κοτόπουλη σούπα" - "η σούπα" is feminine, so "κοτόπουλη", as an adjective, concords in number (singular form) and gender with "η σούπα"
I can understand "η σούπα κοτόπουλου" - "το κοτόπουλο" gets in genetive case by analogy with "ο χυμός πορτοκαλιού".
But what part of speech is "κοτόπουλο"?
Sorry for my meticulousness in attempt to understand the logic of this linguistic construction.
Η σούπα κοτόπουλο is short of η σούπα με κοτόπουλο (soup with chicken). Η σούπα κοτόπουλου is right also. Κοτόπουλο is a noun so it does not become κοτόπουλη etc. It is rare that someone says η σούπα κοτόπουλο or η σούπα κοτόπουλου but both are valid. It is more common to say "κοτόσουπα". But this construction is common for other foods such as "τάρτα κεράσι" cherry pie, "χυμός πορτοκάλι" orange juice so the nominative is also valid unless the noun that characterizes is in the plural, then only genitive is used. P.e You cannot say "κέικ φρούτα" for fruit cake. The right is "κέικ φρούτων". But "κέικ πορτοκάλι" is right. I hope i didn't confuse you with too much info.
First of all, κοτόπουλο is a noun and as a noun it has a grammatical gender that is neutral. As such it will always by κοτόπουλο. I like troll1995's explanation that as a noun characterizing another noun is acting like an adjective and for this reason it comes after the noun that is being characterized. Examples I can think of: "ο καλός λύκος" = "the good wolf" but "Ο λύκος φάντασμα" = "the ghostly wolf"
In my opinion it would be easier to introduce expressions such as σούπα με κοτόπουλο or χυμός από πορτοκάλι and then tell us that it is possible (or customary) to omit the με resp. the από. These two examples left me completely bewildered until I read this discussion.
Doesn't pedagogy go from simple towards complex?
I would argue that pedagogy should go from common (usage) to detailed (grammar), not the other way around.
First you want to learn to speak, to express yourself meaningfully. Then you get into grammatical details, as far as I'm concerned.
Sure, as a foreign adult, starting from Grammar may work for you, but not for a native (child). That's why, for me learning κοτόσουπα first is the most expressive and educational of the choices.
It's καλός λύκος because the adjective must be masculine because the noun λύκος is masculine too. Well we call bear dogs αρκουδόσκυλα. Word to word translation don't always work. Keep in mind that you place the characterizing noun after the characterized one and mostly in the genitive. Orange juice=Χυμός (από) πορτοκάλι=χυμός πορτοκαλιού, chicken soup=Σούπα (με) κοτόπουλο= σούπα κοτόπουλου. But It's not right to assume that because in English a "bear dog" is two words, it has to be so in Greek, or that it is described the same way.