Divulge: transitive verb : to make public; to make known( as a confidence or secret ).
From ” A Rose For Emily” by William Faulkner, ” He would never divulge what happened during that interview but he refused to go back again”.(Page 4, paragraph 13).
Now i understand that the talk between the Baptist minister and Miss Emily Grierson he doesn’t want speak about with anyone else. He’s being respectful and keeping it confidential.