And yes, my teacher is indeed a native German speaker - although it's of course possible that English is another native language, but I doubt it.
Well, there's the possibility of "des Mannes Gesicht". However, although it's completely right - actually it's even better than many other solutions -, you would never use it - it sounds like 300-years-old German.googleearth wrote: I happen to know that Callid is German, so I'm guessing that his teacher is a native German speaker, just like mine. Our teacher also always tells us to rather use the genitive than some of-construction. I don't know whether he'd go so far to declare "face of the man" grammatically wrong or if he'd just leave it as bad style, but he does always tell us that many German students tend to make these "mistakes" because every possible way to phrase this in German would put Gesicht (face) in front of Mann (man). I think that's why here in Germany it's considered mistake while in other non-English-countries it's rather bad style. That actual English native speakers disagree with our teachers on that doesn't seem to bother them.
It seems you're just gonna have to live with them. But it's not like English is the only subject where our teachers should get their facts straight.
Actually, about this problem of genitive and dative, a famous book was written: "Der Dativ ist dem Genetiv sein Tod" (The dative is the death of the genitive) - the title itself shows this problem quite clearly...