“ But Sihon did not trust Israel to pass through his border. But Sihon gathered all his people together, and pitched in Jahaz, and fought against Israel. And Yahweh, the God of Israel, delivered Sihon and all his people into the hand of Israel, and they smote them. So Israel possessed all the land of the Amorites, the inhabitants of that country.”
Jephthah stressed that they had been forced to fight Sihon and the Amorites against their will. But that when they had had to do so, Yahweh had delivered it into their hands. It had thus clearly been Yahweh's intention that they should have the land. So they had divine rights to it. Then he carefully stressed that it was the Amorites who were the actual inhabitants of the country at that time, not the Moabites, so that Israel had not taken it from Moab but from its inhabitants, from the Amorites.
He also probably hoped that the king of Ammon would note in passing what had happened to Sihon and the Amorites as a result of them confronting Yahweh.