In Chapter 16, Duncan tells Munro that he wants to marry Alice, not Cora. Munro takes the opportunity to fill Duncan in on the girls' origin stories, opening the flashback with a metaphor:
“You would be my son, Duncan, and you’re ignorant of the history of the man you wish to call your father. Sit ye down, young man, and I will open to you the wounds of a seared heart, in as few words as may be suitable.”
Munro tells Duncan that he is about to "open to [him] the wounds of a seared heart." He is not opening any physical wounds, but the metaphor makes clear to Duncan and the reader that Munro is about to reveal some intense emotional baggage. As he goes on to tell Duncan, he once fell in love with an Englishwoman named Alice Graham, but he gave up the chance to marry her because the marriage would not have been financially or socially advantageous for her. Instead, he went to the West Indies and married a woman descended from enslaved people. Cora is the child of his first marriage. After that wife died, he returned to England and found Alice Graham still unmarried. He married her and had a daughter, also named Alice, before losing this wife as well. Alice Munro is the image of her mother and the only reminder Munro has of the love of his life.
Munro's intense attachment to his daughter Alice does not seem all that healthy by modern standards, but it explains why he is taken aback by Duncan's announcement that he wants to marry her, not Cora. It is important to note the context in which this vulnerable flashback comes up. Munro only opens up his emotional "wounds" as a practical matter, when they are relevant to the business of marrying off his daughters. In the context of the novel and colonial culture, this display of emotion would not be appropriate for one man to offer another out of the blue. Discussing the women as daughters and potential wives gives Munro and Duncan the opportunity to share their feelings and biographical details, and to grow as characters.