A nuclear scientist once explained this to me and a few of my friends in such a great way and I can only do injustice to that explaination, but I will try anyway.

What the nuclear disasters are, are tail risks. What he meant by that, is the more severe a disaster is the less chance it has happening, which you can imagine like the tail of a rat: the further away it is from body the thinner it is. Now the thing about nuclear disasters is that the tail is very long and gets very thin towards the end. That makes it so most incidents reported are incredibly unintresting (thankfully), most of them being non-vital valves gettint stuck and such. But when those really small (and with advancement always shrinking) chances cause a disaster you may have to evacuate a town. Then he told us about the Eschede train disaster. What happened was basically that a wheel of a train cracked and through incredible unluck killed half of the passangers. And looking at the history of trains, while this particular kind of mishap is very rare and we even have systems in place to prevent it from happening, other kinds of catastrophic failures have happened multiple times throughout history, sometimes even killing bystanders, much like a nuclear reactor could. This didn’t stop people from boarding trains though, since the odds were always in their favor and the usefullness of the train was incredible at the time. At the end of the day we have to evaluate whether the benefits are worth the risk. And once again this scientist told us that while he may be a bit biased in this regard he does think those disasters are less and less likely to happen by the day and with the amount of energy generated they are quite worth it.