There are several reasons I believe people are scared of nuclear power:
1. Nuclear explosions/bombs are linked in peoples minds to nuclear power plants, even though it is physically impossible for a nuclear reactor to have a nuclear detonation. If people thought of napalm every time they filled their car with gasoline we would probably have no combustion engine automobiles.
2. People do not understand how nuclear power plants operate and people fear the unknown. If we did a better job explaining the basics of nuclear power, in simple language, fewer people would be afraid.
3. People believe nuclear power is not "natural" and as such dangerous. They are unaware of the naturally occurring reactor that was discovered to have been in operation underground in South Africa thousands of years ago.
4. Activists have been fear mongering to dupe people out of their hard earned money for decades. They have made their living on perpetuating the fear.
5. People believe that nuclear power plants are not 100% safe, and they are right, nothing is 100% safe. Di-hydrogen Monoxide (DHMO) is objectively one of the deadliest substances known to man, but to ban it is sheer idiocy. Nuclear power is however one of the safest technologies ever used to produce electricity, which has saved countless lives preventing lung disease, hypothermia, and provided a standard of living better than any in history. There has to be a risk/benefit analysis with nuclear power, like DHMO, the benefit far outweighs the risk.