Final answer:
Ji-li's voice broke when she looked in Teacher Gu's eyes because of the emotional connection and intensity she felt in that moment.
Step-by-step explanation:
Ji-li's voice broke when she looked in Teacher Gu's eyes because she felt a connection and a sense of understanding with him. This can be seen in the text when it says, "And she found it strangely embarrassing to meet the child's gaze." It suggests that Ji-li's emotions overwhelmed her, causing her voice to break.
Furthermore, the text also mentions, "It seemed to her that Fay's violet eyes looked through her with piercing wisdom." This implies that Teacher Gu's eyes held a certain kind of power and sincerity that affected Ji-li deeply, causing her voice to break.
In conclusion, Ji-li's voice broke when she looked in Teacher Gu's eyes because of the emotional connection and intensity she felt in that moment.