When Rin killed the dragon, the only option he had was to leave. There was no doubt that the dragon king was not going to retaliate.
The dragon king was first going to go after him and kill him. And when that was done, the dragon king would then unleash his attack on the whole kingdom.
Rin, at this point, was the most wanted man in the whole nine kingdoms. That was why his siblings couldn't hide their sadness and that was why his father, equally, couldn't hide his anger.
They were sending Rin in harm's way. And there was nothing they could do about it. It was the law, and Rin had to abide by it.
Instead of leaving of his own accord, he was banished instead. And banishment was not a good thing.
Rin's mind was heavily occupied with how things had turned out in the last few days. He remembered the day he begged his father to keep to his promise.
He was very angry that his father had not kept to his word but he didn't like how he was forced to leave Atlantia.