Why is "svuj" not used here?

Is this a threat, Duolingo? / Je to hrozba?, Duolingo? ;-)

Help me out here. The Tips & Notes on Possessives say "Svůj very loosely corresponds to the English “own” and indicates the possession by the subject of the clause." Here, the subject is "you", and the object is "your father". The subject is indeed doing the possessing. So why am I unable to get a correct answer when I use svůj? In other lessons, it's marked wrong if I use můj or tvůj when I should have used svůj, so they're clearly not completely interchangeable. What's the actual rule?