What does Mark 6:26 mean?In the story of Esther, King Ahasuerus is manipulated by Haman to send a decree that allows his people to destroy the Jews. Ahasuerus doesn't realize that his queen is Jewish until the decree has been sent out. When Esther reveals her ethnicity, Ahasuerus immediately hangs the evil Haman, but he cannot take back the decree, "for an edict written in the name of the king and sealed with the king's ring cannot be revoked" (Esther 8:8).
Herod Antipas finds himself in a similar situation. Possibly while drunk, and probably while aroused, he has promised his wife's daughter anything she asks in front of "his nobles and military commanders and the leading men of Galilee" (Mark 6:21). Antipas is a Samaritan/Edomite chosen by the occupying Roman emperor to rule over Jews. He built his capital on a cemetery, making it unclean for the Jews, and broke the Jewish law by marrying his brother's wife. He needs all the support he can get, especially if the people revolt (Matthew 14:5). So when his step-daughter publically requests the head of John the Baptist, in response to his own oath, he has to acquiesce.
Unlike Ahasuerus, Antipas is not acting out of a moral obligation to keep his word—he broke his first marriage oath quickly enough. However, he is very concerned about his reputation in front of these nobles, even if earning that support risks rebellion by the people. A similar situation will arise when Pilate agrees to have Jesus crucified to keep the peace (Mark 15:15).
Fear of rebellion is not the only reason Antipas hesitates. He seems to genuinely like John, for whatever reason. "Sorry" is from the Greek root word perilupos and means to be very sad, overcome with sorrow. It is found in Mark only twice—here and of Jesus at Gethsemane (Mark 14:34).