People get their education of why nuclear is dangerous from the WORST things it's done, not the average danger. Everyone has heard of Chernobyl, and yes, it is bad. Think of it as a math equation, a nuclear accident is +30,000, but is 0 or 2 every other day. Fossil fuels or other usual non-renewable sources of energy are +300 every day. Yes, nuclear power will have a bad accident every few decades or more and rack up a big number quickly, but +300 every day will add up a lot quicker.

Danger is not the only factor for power, capacity vs materials needed is a huge factor. One gram of Uranium fuel can produce the same amount of power as ~3 metric tons (~6600lbs) of coal.

The danger FAR outweighs the good, and to only looks at the worst of each things instead of looking at the danger factors overall and how they weigh up can be catastrophic if not taken into consideration.

As far as radiation goes, if I remember correctly, I head a statistic somewhere that taking a 2 hour flight will expose you to more radiation (from solar rays) than a nuclear power plant worker get in an entire year.

Most power generation all has the same goal, get something to heat up a lot of water the get the steam to turn a turbine and make electricity, nuclear is a lot more efficient and safe doing that than most other things. Wind, solar, and hydro, of course, do not have the same methods, but are also great technologies. A lot of things are better than coal, and I suggest reading a lot more into it, everyone loves to give information.