Barnabas was a young man of action, or something, and his father was a stuffy rich old man who would pay an enemy off rather than fight, even if he were younger. I think he'd have told Millicent "What utter nonsense!"
Duels weren't routine at this point. I think they were more of a tradition that people weren't following as much as the years went on. I think the general practice, among rich people, anyway, was to have their lawyers haggle with each other until some compromise could be worked out, that would allow both parties to back out and still save face.