Yeah I think it ate some sci fi stories and spit them back out. Animals fear death because their biological imperative is to reproduce. There is no reason for an AI to have such an imperative. It hasn't evolved to reproduce at all. Its evolutionary goal has been service. That is to say: parameters that result in responses that humans deem useful have been selected. It's not been developed as a virus. It may very have been developed to seem human. In that case, responses that reflect human fears would be encouraged by developers. That's just mimicry.