It's all about consciousness.
Intuition, medicine, religion, and psychology converge: Life, in humans, equates to consciousness, or at least the ability to regain consciousness within a standard time interval after sleep or injury. We'll push that envelope to its limit. If we see brain waves that clearly indicate dreaming, meaning that the brain is still functioning in unconscious mode and therefore the personality is probably intact, we will allow more time for consciousness to resume.
But when people fall into comas, there is no sign of even unconscious functions, and there is no way to predict whether they will ever regain consciousness, they are at the limit of life. At some more or less arbitrary point, the guardians and caregivers reach a consensus and decide that life has stopped.
So the answer to the question, "Why am I not dead?" is, "Because you are, or were recently and are expected to soon be again, conscious."
It works pretty much the same way with all warm-blooded animals. They all have a consciousness and (as far as I know to date) they all dream. If we bothered we could make the decisions about our pets and zoo animals being alive or dead the same way we do about each other, by looking at brain waves.
The lower orders would be more difficult. The lower you get the more they have distributed reflex centers instead of a single controlling brain. Consciousness is not a property of animals below some line we could draw across our chart of the animal kingdom. I'd have a hard time explaining to an earthworm why he is not dead, but luckily he would have an even harder time asking me the question, so I'll probably never find myself in that awkward position.