The program hangs on `cin.getline()` due to improper use of `cin.ignore()`, which is intended to clear the input buffer. When `cin.ignore()` is called without arguments, it can lead to unexpected behavior if the buffer is empty, causing the program to hang. The user incorrectly assumes that placing `cin.ignore()` before every `cin.getline()` is necessary, but this can disrupt the flow of input. Debugging efforts are ineffective as the program does not return from the `cin.ignore()` call. Proper understanding of `cin.ignore()` and its parameters is essential to avoid these issues.