I'm damn sure there isn't an elephant in my house.
I know what elephants look like. I know how large they are. I've checked every area where an elephant would fit. So it's reasonable for me to say "There's no elephant in my house."
But not if I thought like a religious believer. Because then I could argue, "Yes, there's an elephant in my house, because..."
It's an invisible elephant.
I'm the only one who can see it.
I can sense the elephant even if no one else can.
Its disguised as an ordinary object.
There are other possible delusions that follow the "because."
I just listed a few to give you an idea of how religious people justify a faith-based belief in God, spirit, soul, life after death, or other supernatural stuff in the same way a deluded person might argue "there's an elephant in my house."
This analogy is contained in Guy Newland's "Introduction to Emptiness," one of the best books about Buddhism I've ever read. (And I've read quite a few.)
Buddhist emptiness is the entirely scientific notion that nothing has an intrinsic nature or inherent existence. Here's how Newland defines these terms.
emptiness: the sheer nonexistence of intrinsic nature. For example, the table's emptiness is the table's lack of existence by way of an intrinsic nature.
intrinsic nature: an essential nature whereby something comes to have an independent way of existing without being posited through the force of consciousness. The sheer absence of this is emptiness.
inherent existence: the existence of something by the power of its own intrinsic or essential character.
The elephant in the room, then, is akin to a deluded belief in something that is absolutely independent, eternal, unchanging, possessing intrinsic nature. Examples include traditional religious beliefs in God, soul, spirit, and such -- entities that are everlastingly separate and distinct from ever-changing material reality.
Problem is, they don't exist. Just like a elephant in a house that doesn't contain an elephant. Newland writes:
That cars and tables, people and schools are devoid of any trace of analytically findable nature does not mean that they do not exist. Clearly they do exist. But what kind of existence can things have when they have no shred of evidence from their own side?
As we have seen, things exist as dependent arisings, phenomena that exist only through their interconnections with other (equally empty) phenomena.
...The point is that we must notice within our own experience the ignorance that is the root of our cyclic existence, our own misconception of ourselves as having intrinsic nature.
Then, we have to set before ourselves a limited but comprehensive set of alternatives for how such a nature might exist if it did, in fact, exist. As an analogy, suppose someone was suffering from the delusion that there was an elephant in the house.
We could make a comprehensive list of all the rooms in the house, or perhaps a list of all the spaces in the house that might in any way be large enough to contain an elephant. Then we could ask the deluded person to set it very firmly in mind that, were there an elephant in the house, it would absolutely have to be in one of those rooms.
If he had some doubt, then we could add more places to the list, even if they seemed logically unnecessary, until he was able to feel decisively confident that any elephant located in the house would have to be in one of those places.
Then, when a search of each room turned up no elephant, the force of his sense that, "There is simply nowhere else for an elephant to be" would be converted into the realization that, quite contrary to his delusion, there is no elephant in the house at all.
Again, for Buddhism (as for modern neuroscience) the "elephant" is the mistaken belief in an enduring, independent self, known as soul in many religious faiths. More broadly, it is the belief that anything at all possesses an intrinsic nature that's divorced from interdependence with other entities.
The metaphor is limited, of course. Elephants have what Newland calls a "conventional nature." Meaning, they actually exist, though not as beings with an intrinsic nature. So it is possible to find an elephant in one's house, albeit unlikely.
But in the case of imaginary religious entities like God, soul, and spirit, there is no evidence that these things even exist conventionally.
So there's a double delusion involved with them: first, they don't exist; second, even if they did exist, they wouldn't exist as entities with an unchanging intrinsic nature -- eternal, immortal, separate from material reality.