For Herod himself had sent men who arrested John, bound him, and put him in prison on account of Herodias, his brother Philip’s wife, because Herod had married her. For John had been telling Herod, ‘It is not lawful for you to have your brother’s wife.’ And Herodias had a grudge against him, and wanted to kill him. But she could not, for Herod feared John, knowing that he was a righteous and holy man, and he protected him. When he heard him, he was greatly perplexed; and yet he liked to listen to him. (Mark 6: 17-20)

Herod Antipas married his niece (not a problem at the time) who had quite recently been his sister-in-law. Marrying a sister-in-law - except in special circumstances after a brother's death - was considered incest.

John the Baptist caused political unrest by criticizing the incestuous marriage. John was arrested to quiet this criticism. But otherwise Antipas seems to have appreciated John. The intense integrity of John probably intriqued Antipas.

Some of the most poignant figures in history and literature are self-aware realists. They are considered "realists" because they unstintingly pursue self-interest. But they bring to this self-interest a dispassionate even self-critical detachment.

Antipas held no grudge against John's criticism. He simply needed to quiet the criticism. Antipas protected John from his less-restrained wife. It is even possible that he came to see John as a kind of alter-ego.

What would motivate an intelligent and capable man to consistently behave against his self-interest? John pursued a purpose that seemed to contradict self-interest. That must truly have perplexed Herod Antipas.