This is from the Kubernetes saying of "treat servers like cattle, not pets". Of course, some people like me keep cattle as pets, but then again I also name my servers, even the virtual or containerised ones.
That (unpleasant) saying predates Kubernetes by at least half a decade.
Yeah that was indeed the inspiration (though I'm pretty sure it predates Kubernetes!) but the juxtaposition with "terminate" is unfortunate.