Im pretty sure that it’s B. Because in academic writing you should give attention to all sides of the issue.
I believe the answer is: A. "I am sorry," he said, and patted me on the shoulder with his good hand. "I would not be rude. My wife has just died. You must forgive me."
The word resign indicates accepting some sort of feeling or situation that cannot be ignored or pushed aside. From the sentences in option A, we can infer that the reader already accept the fact that his wife has died and acknowledge that his emotion is influenced by it.
