More than poetic, it's very real. It's called PCD, programmed cell death, and it affects most life on earth. But not all life. It is terminal, and it is an affliction which will kill you. So, yes, we're all terminally ill. Make the most of your time. We are all dying.
Life has proved fatal to all but 6-7% of us humans so far. And there isn't any indication that the current remaining will escape it's touch.