Obadiah is a national oracle, or prophecy against Edom. Edomites are descendants of Esau. Jacob and Esau had struggles even in the womb of Rebekah. The day of Lord is coming to Edom because of their pride & their violence to their brother, Israel. They gloated on the day of misfortune, they rejoiced on the day of destruction, and they boasted on the day of distress. There is no call for repentance in this prophecy, and partly because the message of hope was for Israel that God sees and knows, and He will fight for His children, in HIS time.
