Death is when the mortal body stops living. It is a death and those who died this death are called "the dead" despite having a living soul and spirit.
When the bible speaks of the saved never dying, it is a reference to full and complete death, the second death, where body, soul and spirit are no longer alive.
I used to say the same thing, but I realize now that I was only saying it because it was the only way I could make sense of things. I had to believe that it referred to the second death, and so I convinced myself that this was true. Now I realize there's a much better explanation, which I've been trying to show you.
The fact is, dead is dead. Like a door knob. No consciousness. King Solomon said the dead know nothing, and he was right. That is death. Living on in spirit form is not death. That's life. Until you accept the definition of death, you will never make sense of it. So please understand what "dead" actually means. It means you have no consciousness. If you have consciousness, you are not dead. It's as simple as that.
And no, you can't say our body is dead but our spirit is alive, because we are not two parts that exist independently of each other. We are our consciousness, whether that consciousness is in a physical form or a spiritual form, there is still only one consciousness, and wherever that consciousness is, you are. If your consciousness is in spirit form, then
you are a spirit, not a physical body, so even if the physical body is dead, you can not say that you are dead, because
you are not that body.