Why would we read Rus on Shavuos? In fact why would we read it at all?? It reveals the humiliating story of the roots of our eternal kingdom. Elimelech should have been the father of the Melucha. Instead due to his reluctance to deal with his people's plight, the entire Malchus Bais Dovid was handed over to a gentile woman who came from a people that were not even allowed to marry into our holy nation.
The Nachlas Yosef answers that on the day of Kabalas Hatorah, Chazal are trying to teach us a valuable lesson. There is only one thing in this world and that is Chesed. "Olam Chesed Yibaneh". So to Chazal tell us, the Torah starts with Chesed (creation) and ends with Chesed (Hashem buries Moshe) and is Chesed through and through.
On the day of Kabalas HaTorah we read Megilas Rus to teach us two great lessons on Chesed. How far the great will fall without chesed and how the low will rise to great heights through Chesed. Elimelech was the heir of Malchus Bais Yehuda. He had it all, torah, yiras shamyim, and wealth. He was the hope and dream of Klal Yisroel. Unfortunately his weakness was in a very critical trait, Chesed. This slight failing destroyed everything and rendered him a footnote of history.
Rus, a woman from the hated selfish nation that is even forbidden to assimilate into Am Yisroel, was the epitome of Chesed. She was the daughter of the king yet she followed her destitute widowed mother in law to a foreign land without any justification or motive. No matter who she was or where she came from, she is the matriarch of all of Klal Yisroel's hopes and dreams.