It is generally accepted that all cyber attacks cannot be prevented, creating a need for the ability to detect and respond to cyber attacks. Both connectionist and symbolic AI are currently being used to support such detection and response. In this paper, we make the case for combining them using neurosymbolic AI. We identify a set of challenges when using AI today and propose a set of neurosymbolic use cases we believe are both interesting research directions for the neurosymbolic AI community and can have an impact on the cyber security field. We demonstrate feasibility through two proof-of-concept experiments.