Neurons in your brain would need to be both able to replace themselves, and then most importantly, spread their axons and dendrites to the appropriate location. Brain cells are a small cell body coupled with long tentacle like structures that stretch from place to place to form connections. This means that in a place like your spine, a single cell goes all the way from your brain to your tailbone, which means that the cell is about a meter long! Its easy enough for a new cell body to be put in the same place if the original gets damaged, but it would be very hard to make sure that cell then grew that extreme distance and connected back to the correct target.
There are some animals that have very impressive regenerative properties, but it just isn’t something humans (or most mammals) are capable of. In the ancestral environment, an accident that was bad enough to leave you paralyzed was generally bad enough to kill you pretty quickly, which means that we never evolved a way to regenerate that kind of damage.
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