I could have hugged Dumbledore. Instead, I hugged myself in sheer glee. In its way, it was a masterstroke! Not only had he thwarted Umbridge over getting rid of Trelawney, but Firenze, being a "half-breed," was bound to get right up her nasty nose. And, as a centaur, he did know his stuff on Divination, unlike Trelawney, so she couldn't sack him for incompetence.