Why is it "du"? I thought it means "of the", not "to the". Why doesn't "à la" work?
The French language considers the key as belonging to the office, not as its destination.
La clé est à moi? Ou bien c'est au bureau?
"Ma clé du bureau" means that you have one of the keys opening the office (and still belonging to the office).
In English we say the key to a room, but in French we say la clé d'une pièce.
Using à would make no sense here (and if it did, it would be "au" and not "à la")