Question: Why would Jesus tell a story of human spirits surviving death if this is false doctrine?
It isn't "annihilation" if there isn't something being destroyed. Consider this: when you die, your "voice" isn't being destroyed. Your voice feels like an ethereal thing without substance, but science has given us the ability to see it for what it really is, a compression of air waves caused by vibrations in your voice box. You can record your voice on a device sensitive enough to pick it up because it has physical substance. The same is true of your thoughts, which are merely firings of neurons in certain patterns. It "feels" like an ethereal, mysterious spirit but your thoughts can be seen with a device sensitive to picking it up (an FMRI). This is obvious when your brain malfunctions -- problems like amnesia don't make sense when your memory is seen as a soul-function, but make perfect sense when seen as a function of the brain.
So, when your body dies, nothing lives after it because there is simply nothing there to live after it. Jesus didn't know better in the same way that you don't know better, and it's no more mysterious that he believed in souls than it is that you do, and needs no more explanation than your own belief.