The conviction that this human showed couldn't help making Drogath hesitate.
However, there was no going back for him.
The moment that I had chosen to do this in public, he was already doomed to accept.
After all, if he backed down now after everything that would happen, he would be known as a coward for the rest of his life. So he was already trapped in a corner unless he was able to talk his way out of it.
Drogath narrowed his eyes to look at him before saying, "You think that you can get out of the promise of giving your head since you're a guest of our king, don't you? You want to make fun of us dwarves?"
He was trying to use both logic and emotion at the same time.
He used the logic of him being guests of the Dwarven King to break a promise while also invoking the emotions of the dwarves around him.
But I smoothly shut it down by saying, "Do you want it in writing?"