(based on Siach Shaul, Yamim Noraim p. 314-6)

The choice of Sefer Yonah to be read towards the end of the holy day of Yom Kippur is, on the simple level, due to the great success of the teshuva of Ninveh. However, the fact that the entire book is read hints at another idea, which is perhaps actually the main one.
Yonah ben Amitai was given a mission by Hashem, and he naively tried to avoid it. Hashem sent a more obedient messenger, the wind, and it instilled fear in the passengers of the boat. The Yalkut Shimoni says that there were members of each of the 70 nations on that boat. Each one prayed in his own way to his god for the same thing – to live rather than die. Only one person from one nation was apathetic, sleeping in the bottom of the boat without praying. Yonah knew the truth and tried to ignore it, until his counterparts exhorted him to join in prayer. Yonah told them there was a simpler solution – simply throw him overboard.
It his not hard to come to the conclusion that although Yonah was a real person, the whole story is a parable in its essence. Bnei Yisrael are compared to a yonah (dove) (Berachot 53b). Yonah was the son of Amitai, reminiscent of the father of Bnei Yisrael, Hashem, whose seal is that of emet (truth). Like Yonah, we are sent to fix the world so that it will accept the kingdom of Hashem, and we avoid the task. There are great storms around us, and while the nations are not all proficient at it, they pray. It is possible that when the nations opened their session in silence, there was real prayer, because even those who possess nuclear weapons want to live. [Perhaps this is a reference to the Windscale nuclear disaster in England, which took place in 1957, although a few days after Yom Kippur.]
In difficult situations, there is one nation that tries to avoid the spotlights but does not succeed to avoid them. "Lots are cast" and Israel comes up being singled out. The world looks around and points to the Middle East, and then within the Middle East they point to us, to Israel.
"Contemplate the years of every generation" (Devarim 32:7). This country and this region has been sleeping for many centuries. This point, at the edge of the desert, suddenly arose as if from the dead. Sheiks woke up and decided that this is indeed a desirable place, in a strategic location. What caused the storm that awoke people? Israel.
What prodded Egypt to seek so many weapons? What unites all the wild nations? Who riles everyone up? It is Israel. And when they cast lots, who do they find is guilty? Israel. Indeed it is true that disaster befalls the world because of Israel (Yevamot 63b).
Are we able to understand what the nature of the disaster is? Should we wait to see if they will throw us into the sea? Sometimes we think that we are not able to do anything. Our arms do not extend far enough, and we do not determine what our nation does. The Rambam (Teshuva 3:4) teaches us that we can view the world as being at a standstill, and the actions of one person – indeed, our own – could possibly determine the future of the world. If Israel is in the middle of what happens in the world, it is every individual who, in his own way, is in the center.