The article advises new managers not to joke about firing people, as it can be perceived as insensitive and unprofessional. This is because, as a manager, one has a significant amount of control over their employees' lives, and joking about termination can cause stress and uncertainty. The article emphasizes that the ability to terminate someone's employment is a serious matter and should be treated with respect. Managers should be mindful of their words and actions, especially when it comes to sensitive topics like employment security.