Fallacies are mistaken beliefs. Things that people believe in that don't make sense. In this passage, the narrator is saying to another person that all people should support veterans(people who were in a war) because their grandfather was killed in World war 2. But, that means that the grandfather was <em>killed by a veteran</em>! This doesn't make sense. The fallacy is that veterans should be supported.
Jing-mei wanted to show her gratitude to Mr. Chong. So with her mother's permission and her help she decided to give to her old almost deaf teacher the piano as a present.