With the popularity of AI-infused systems, conversational agents (CAs) are becoming essential in diverse areas, offering new functionality and convenience, but simultaneously, suffering misuse and verbal abuse. We examine whether conversational agents' response styles under varying abuse types influence those emotions found to mitigate peoples' aggressive behaviors, involving three verbal abuse types (Insult, Threat, Swearing) and three response styles (Avoidance, Empathy, Counterattacking). Ninety-eight participants were assigned to one of the abuse type conditions, interacted with the three spoken (voice-based) CAs in turn, and reported their feelings about guiltiness, anger, and shame after each session. The results show that the agent's response style has a significant effect on user emotions. Participants were less angry and more guilty with the empathy agent than the other two agents. Furthermore, we investigated the current status of commercial CAs' responses to verbal abuse. Our study findings have direct implications for the design of conversational agents.