Verbal abuse is a hostile form of communication ill-intended to harm the other person. With a plethora of AI solutions around, the other person being targeted may be a conversational agent. In this study, involving 3 verbal abuse types (Insult, Threat, Swearing) and 3 response styles (Avoidance, Empathy, Counterattacking), we examine whether a conversational agent's response style under varying abuse types influences those emotions found to mitigate people's aggressive behaviors. Sixty-four participants, assigned to one of the abuse type conditions, interacted with the three conversational agents in turn and reported their feelings about guiltiness, anger, and shame after each session. Our study results show that, regardless of the abuse type, the agent's response style has a significant effect on user emotions. Participants were less angry and more guilty with the empathetic agent than the other two agents. Our study findings have direct implications for the design of conversational agents.