Why isn't Hawking radiation emitted by every massive body? (because every massive body causes deformation of space-time, and this causes the vacuum state to be observer dependent, if I'm not wrong)
What makes black holes special in this context? Does it have something to do with the existence of a singularity/event horizon? (Why is that an important ingredient?)
It's not unique to black holes. An accelerating observer would also experience a thermal radiation. This is called the Unruh radiation and is essentially equivalent to Hawking radiation. What's important is that when we have different choices of what we can call the vacuum in some spacetime, one particular vacuum state can be a thermal state seen by an observer who has another vacuum choice.
EDIT: What's common between acceleration and black holes is that they have a horizon. The existence of horizon makes you inaccessible of the information on the other side of the horizon. Basically it's this ignorance that leads to a thermal state.
