Here's why:
* Mass: Neutron stars are formed from the collapsed cores of massive stars, at least 8 times the mass of our Sun. Our Sun is simply not massive enough to undergo the same kind of catastrophic collapse that creates a neutron star.
* Evolutionary Path: The Sun will evolve into a red giant, then shed its outer layers, leaving behind a white dwarf. White dwarfs are much smaller and denser than neutron stars, but still significantly larger than the Sun's current size.
Instead of becoming a neutron star, the Sun will end its life as a white dwarf. This process will take billions of years.