Conversational robots (chatbots) are currently an extended Insurtech that is widely used to enable policyholders’ communication with insurance firms. This paper analyses customers’ acceptance of chatbots in procedures with regard to in-force policies. We analysed a semistructured survey answered by workers of a public Spanish university. Structured questions have been grounded in the well-known technology acceptance model (TAM), which is based on two explanatory variables: perceived usefulness (PU) and perceived ease of use (PEOU). We have also considered two additional explanatory factors: social influence (SI), whose impact on behavioral intention (BI) is mediated by PU, and trust (TRUST), whose influence on BI is supposed to be made throughout PU and PEOU. Likewise, we asked two open questions about the advantages and disadvantages of chatbot use to make procedures linked with in-force insurance contracts. We performed our analysis by using quantitative and qualitative methods. The quantitative analysis tests the suitability of TAM on our data and has been performed by using structural equation modelling with partial least squares (PLS-SEM). Subsequently, to reach a deeper understanding of the reasons that explain the respondents’ behavioral intention, we provide a systematic overview of the answers to open questions with the help of the groundwork provided by TAM. We have checked that the basic TAM along with social influence and trust provide a satisfactory explanation for behavioral intention toward bots. Likewise, we have observed a general reluctance toward the use of chatbots. The qualitative analysis showed that arguments explaining resistance come from all explanatory factors considered in the paper. Therefore, mainstream responses have outlined that interaction with chatbots is difficult, and many times, the procedure must be finished with the assistance of a human operator. Likewise, many responses point out as a relevant drawback that they provide a dehumanized service without empathy. Consequently, interactions with chatbots are perceived as cumbersome, ineffective, and a loss of time. Although some people perceive that the faster service provided by chatbots in concrete circumstances is an advantage, other theoretical consequences that may add value, such as temporal flexibility and the possibility of proving better services with the same cost and/or reducing insurance prices because of the reduction of firms’ administrative costs, are generally not perceived. Our findings have theoretical and practical implications. We have shown that TAM provides a reliable theoretical model to understand policyhoders’ acceptance of chatbot technology in an insurance setting. Perceived usefulness, reliability, social opinion about bot adoption, and usability must be improved to avoid generalized policyholders’ reluctance. That resistance is because of issues such as conversational skills, the capability to provide an interaction closer to being human, and users’ perception that chatbots actually add value to policyholders.